textual presentation in statistics meaning

• Accountancy
• Business Studies
• Commercial Law
• Organisational Behaviour
• Human Resource Management
• Entrepreneurship
• CBSE Class 11 Statistics for Economics Notes

Chapter 1: Concept of Economics and Significance of Statistics in Economics

• Statistics for Economics | Functions, Importance, and Limitations

Chapter 2: Collection of Data

• Data Collection & Its Methods
• Sources of Data Collection | Primary and Secondary Sources
• Direct Personal Investigation: Meaning, Suitability, Merits, Demerits and Precautions
• Indirect Oral Investigation : Suitability, Merits, Demerits and Precautions
• Difference between Direct Personal Investigation and Indirect Oral Investigation
• Information from Local Source or Correspondents: Meaning, Suitability, Merits, and Demerits
• Questionnaires and Schedules Method of Data Collection
• Difference between Questionnaire and Schedule
• Qualities of a Good Questionnaire and types of Questions
• What are the Published Sources of Collecting Secondary Data?
• What Precautions should be taken before using Secondary Data?
• Two Important Sources of Secondary Data: Census of India and Reports & Publications of NSSO
• What is National Sample Survey Organisation (NSSO)?
• What is Census Method of Collecting Data?
• Sample Method of Collection of Data
• Methods of Sampling
• Father of Indian Census
• What makes a Sampling Data Reliable?
• Difference between Census Method and Sampling Method of Collecting Data
• What are Statistical Errors?

Chapter 3: Organisation of Data

• Organization of Data
• Objectives and Characteristics of Classification of Data
• Classification of Data in Statistics | Meaning and Basis of Classification of Data
• Concept of Variable and Raw Data
• Types of Statistical Series
• Difference between Frequency Array and Frequency Distribution
• Types of Frequency Distribution

Chapter 4: Presentation of Data: Textual and Tabular

Textual presentation of data: meaning, suitability, and drawbacks.

• Tabular Presentation of Data: Meaning, Objectives, Features and Merits
• Different Types of Tables
• Classification and Tabulation of Data

Chapter 5: Diagrammatic Presentation of Data

• Diagrammatic Presentation of Data: Meaning , Features, Guidelines, Advantages and Disadvantages
• Types of Diagrams
• Bar Graph | Meaning, Types, and Examples
• Pie Diagrams | Meaning, Example and Steps to Construct
• Histogram | Meaning, Example, Types and Steps to Draw
• Frequency Polygon | Meaning, Steps to Draw and Examples
• Ogive (Cumulative Frequency Curve) and its Types
• What is Arithmetic Line-Graph or Time-Series Graph?
• Diagrammatic and Graphic Presentation of Data

Chapter 6: Measures of Central Tendency: Arithmetic Mean

• Measures of Central Tendency in Statistics
• Arithmetic Mean: Meaning, Example, Types, Merits, and Demerits
• What is Simple Arithmetic Mean?
• Calculation of Mean in Individual Series | Formula of Mean
• Calculation of Mean in Discrete Series | Formula of Mean
• Calculation of Mean in Continuous Series | Formula of Mean
• Calculation of Arithmetic Mean in Special Cases
• Weighted Arithmetic Mean

Chapter 7: Measures of Central Tendency: Median and Mode

• Median(Measures of Central Tendency): Meaning, Formula, Merits, Demerits, and Examples
• Calculation of Median for Different Types of Statistical Series
• Calculation of Median in Individual Series | Formula of Median
• Calculation of Median in Discrete Series | Formula of Median
• Calculation of Median in Continuous Series | Formula of Median
• Graphical determination of Median
• Mode: Meaning, Formula, Merits, Demerits, and Examples
• Calculation of Mode in Individual Series | Formula of Mode
• Calculation of Mode in Discrete Series | Formula of Mode
• Grouping Method of Calculating Mode in Discrete Series | Formula of Mode
• Calculation of Mode in Continuous Series | Formula of Mode
• Calculation of Mode in Special Cases
• Calculation of Mode by Graphical Method
• Mean, Median and Mode| Comparison, Relationship and Calculation

Chapter 8: Measures of Dispersion

• Measures of Dispersion | Meaning, Absolute and Relative Measures of Dispersion
• Range | Meaning, Coefficient of Range, Merits and Demerits, Calculation of Range
• Calculation of Range and Coefficient of Range
• Interquartile Range and Quartile Deviation
• Partition Value | Quartiles, Deciles and Percentiles
• Quartile Deviation and Coefficient of Quartile Deviation: Meaning, Formula, Calculation, and Examples
• Calculation of Mean Deviation for different types of Statistical Series
• Mean Deviation from Mean | Individual, Discrete, and Continuous Series
• Standard Deviation: Meaning, Coefficient of Standard Deviation, Merits, and Demerits
• Standard Deviation in Individual Series
• Methods of Calculating Standard Deviation in Discrete Series
• Methods of calculation of Standard Deviation in frequency distribution series
• Combined Standard Deviation: Meaning, Formula, and Example
• How to calculate Variance?
• Coefficient of Variation: Meaning, Formula and Examples
• Lorenz Curveb : Meaning, Construction, and Application

Chapter 9: Correlation

• Correlation: Meaning, Significance, Types and Degree of Correlation
• Methods of measurements of Correlation
• Calculation of Correlation with Scattered Diagram
• Spearman's Rank Correlation Coefficient
• Karl Pearson's Coefficient of Correlation
• Karl Pearson's Coefficient of Correlation | Methods and Examples

Chapter 10: Index Number

• Index Number | Meaning, Characteristics, Uses and Limitations
• Methods of Construction of Index Number
• Unweighted or Simple Index Numbers: Meaning and Methods
• Methods of calculating Weighted Index Numbers
• Fisher's Index Number as an Ideal Method
• Fisher's Method of calculating Weighted Index Number
• Paasche's Method of calculating Weighted Index Number
• Laspeyre's Method of calculating Weighted Index Number
• Laspeyre's, Paasche's, and Fisher's Methods of Calculating Index Number
• Consumer Price Index (CPI) or Cost of Living Index Number: Construction of Consumer Price Index|Difficulties and Uses of Consumer Price Index
• Methods of Constructing Consumer Price Index (CPI)
• Wholesale Price Index (WPI) | Meaning, Uses, Merits, and Demerits
• Index Number of Industrial Production : Characteristics, Construction & Example
• Inflation and Index Number

Important Formulas in Statistics for Economics

• Important Formulas in Statistics for Economics | Class 11

Presentation of Data refers to the exhibition of data in such a clear and attractive way that it is easily understood and analysed. Data can be presented in different forms, including Textual or Descriptive Presentation, Tabular Presentation, and Diagrammatic Presentation.

Textual Presentation

Textual or Descriptive Presentation of Data is one of the most common forms of data presentation. In this, data is a part of the text of the study or a part of the description of the subject matter of the study. It is usually preferred when the quantity of data is not very large. For example, there are 50 students in a class, among them 30 are boys and 20 are girls. This is the data that can be understood with the help of a simple text and no table or pie diagram is required for the same. 

Suitability

Textual Presentation of Data is suitable when the quantity of data is not large. It means that a small portion of data that is presented as a part of the subject matter of study can become useful supportive evidence to the given text. Therefore, instead of saying that the price of petrol is skyrocketing, it can be said that the price of petrol has increased by 20% in the last 2 years, and this statement will be more meaningful and precise. Under textual presentation of data, an individual does not have to support the text with the help of a diagram or table as the text in itself is very small and has few observations. 

Advantages of Textual Presentation of Data

Textual Presentation of Data has the following benefits:

1. It allows the researcher to make an elaborate interpretation of data during the presentation. 

2. A researcher can easily present qualitative data that cannot be presented in tabular or graphical form using the textual presentation of data. 

3. If the data is present in small sets, a textual presentation can be easily used. For example, there are 50 students in a class, among them, 30 are boys and 20 are girls. This is the data that can be understood with the help of a simple text and no table or pie diagram is required for the same. 

Disadvantages of Textual Presentation of Data

Textual Presentation of Data has the following drawbacks:

1. One of the major drawbacks of the textual presentation of data is that it provides extensive data in the form of text and paragraphs which makes it difficult for the user of data to draw a proper conclusion at a glance. This facility is provided in tabular or diagrammatic presentation of data.

2. This method of presenting data is not suitable for large sets of data as these sets contain too many details. 

3. Besides, one has to read through the whole text in order to understand and comprehend the main point of the data.

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• Korean J Anesthesiol
• v.70(3); 2017 Jun

Statistical data presentation

1 Department of Anesthesiology and Pain Medicine, Dongguk University Ilsan Hospital, Goyang, Korea.

Sangseok Lee

2 Department of Anesthesiology and Pain Medicine, Sanggye Paik Hospital, Inje University College of Medicine, Seoul, Korea.

Data are usually collected in a raw format and thus the inherent information is difficult to understand. Therefore, raw data need to be summarized, processed, and analyzed. However, no matter how well manipulated, the information derived from the raw data should be presented in an effective format, otherwise, it would be a great loss for both authors and readers. In this article, the techniques of data and information presentation in textual, tabular, and graphical forms are introduced. Text is the principal method for explaining findings, outlining trends, and providing contextual information. A table is best suited for representing individual information and represents both quantitative and qualitative information. A graph is a very effective visual tool as it displays data at a glance, facilitates comparison, and can reveal trends and relationships within the data such as changes over time, frequency distribution, and correlation or relative share of a whole. Text, tables, and graphs for data and information presentation are very powerful communication tools. They can make an article easy to understand, attract and sustain the interest of readers, and efficiently present large amounts of complex information. Moreover, as journal editors and reviewers glance at these presentations before reading the whole article, their importance cannot be ignored.

Introduction

Data are a set of facts, and provide a partial picture of reality. Whether data are being collected with a certain purpose or collected data are being utilized, questions regarding what information the data are conveying, how the data can be used, and what must be done to include more useful information must constantly be kept in mind.

Since most data are available to researchers in a raw format, they must be summarized, organized, and analyzed to usefully derive information from them. Furthermore, each data set needs to be presented in a certain way depending on what it is used for. Planning how the data will be presented is essential before appropriately processing raw data.

First, a question for which an answer is desired must be clearly defined. The more detailed the question is, the more detailed and clearer the results are. A broad question results in vague answers and results that are hard to interpret. In other words, a well-defined question is crucial for the data to be well-understood later. Once a detailed question is ready, the raw data must be prepared before processing. These days, data are often summarized, organized, and analyzed with statistical packages or graphics software. Data must be prepared in such a way they are properly recognized by the program being used. The present study does not discuss this data preparation process, which involves creating a data frame, creating/changing rows and columns, changing the level of a factor, categorical variable, coding, dummy variables, variable transformation, data transformation, missing value, outlier treatment, and noise removal.

We describe the roles and appropriate use of text, tables, and graphs (graphs, plots, or charts), all of which are commonly used in reports, articles, posters, and presentations. Furthermore, we discuss the issues that must be addressed when presenting various kinds of information, and effective methods of presenting data, which are the end products of research, and of emphasizing specific information.

Data Presentation

Data can be presented in one of the three ways:

–as text;

–in tabular form; or

–in graphical form.

Methods of presentation must be determined according to the data format, the method of analysis to be used, and the information to be emphasized. Inappropriately presented data fail to clearly convey information to readers and reviewers. Even when the same information is being conveyed, different methods of presentation must be employed depending on what specific information is going to be emphasized. A method of presentation must be chosen after carefully weighing the advantages and disadvantages of different methods of presentation. For easy comparison of different methods of presentation, let us look at a table ( Table 1 ) and a line graph ( Fig. 1 ) that present the same information [ 1 ]. If one wishes to compare or introduce two values at a certain time point, it is appropriate to use text or the written language. However, a table is the most appropriate when all information requires equal attention, and it allows readers to selectively look at information of their own interest. Graphs allow readers to understand the overall trend in data, and intuitively understand the comparison results between two groups. One thing to always bear in mind regardless of what method is used, however, is the simplicity of presentation.

Values are expressed as mean ± SD. Group C: normal saline, Group D: dexmedetomidine. SBP: systolic blood pressure, DBP: diastolic blood pressure, MBP: mean blood pressure, HR: heart rate. * P < 0.05 indicates a significant increase in each group, compared with the baseline values. † P < 0.05 indicates a significant decrease noted in Group D, compared with the baseline values. ‡ P < 0.05 indicates a significant difference between the groups.

Text presentation

Text is the main method of conveying information as it is used to explain results and trends, and provide contextual information. Data are fundamentally presented in paragraphs or sentences. Text can be used to provide interpretation or emphasize certain data. If quantitative information to be conveyed consists of one or two numbers, it is more appropriate to use written language than tables or graphs. For instance, information about the incidence rates of delirium following anesthesia in 2016–2017 can be presented with the use of a few numbers: “The incidence rate of delirium following anesthesia was 11% in 2016 and 15% in 2017; no significant difference of incidence rates was found between the two years.” If this information were to be presented in a graph or a table, it would occupy an unnecessarily large space on the page, without enhancing the readers' understanding of the data. If more data are to be presented, or other information such as that regarding data trends are to be conveyed, a table or a graph would be more appropriate. By nature, data take longer to read when presented as texts and when the main text includes a long list of information, readers and reviewers may have difficulties in understanding the information.

Table presentation

Tables, which convey information that has been converted into words or numbers in rows and columns, have been used for nearly 2,000 years. Anyone with a sufficient level of literacy can easily understand the information presented in a table. Tables are the most appropriate for presenting individual information, and can present both quantitative and qualitative information. Examples of qualitative information are the level of sedation [ 2 ], statistical methods/functions [ 3 , 4 ], and intubation conditions [ 5 ].

The strength of tables is that they can accurately present information that cannot be presented with a graph. A number such as “132.145852” can be accurately expressed in a table. Another strength is that information with different units can be presented together. For instance, blood pressure, heart rate, number of drugs administered, and anesthesia time can be presented together in one table. Finally, tables are useful for summarizing and comparing quantitative information of different variables. However, the interpretation of information takes longer in tables than in graphs, and tables are not appropriate for studying data trends. Furthermore, since all data are of equal importance in a table, it is not easy to identify and selectively choose the information required.

For a general guideline for creating tables, refer to the journal submission requirements 1) .

Heat maps for better visualization of information than tables

Heat maps help to further visualize the information presented in a table by applying colors to the background of cells. By adjusting the colors or color saturation, information is conveyed in a more visible manner, and readers can quickly identify the information of interest ( Table 2 ). Software such as Excel (in Microsoft Office, Microsoft, WA, USA) have features that enable easy creation of heat maps through the options available on the “conditional formatting” menu.

All numbers were created by the author. SBP: systolic blood pressure, DBP: diastolic blood pressure, MBP: mean blood pressure, HR: heart rate.

Graph presentation

Whereas tables can be used for presenting all the information, graphs simplify complex information by using images and emphasizing data patterns or trends, and are useful for summarizing, explaining, or exploring quantitative data. While graphs are effective for presenting large amounts of data, they can be used in place of tables to present small sets of data. A graph format that best presents information must be chosen so that readers and reviewers can easily understand the information. In the following, we describe frequently used graph formats and the types of data that are appropriately presented with each format with examples.

Scatter plot

Scatter plots present data on the x - and y -axes and are used to investigate an association between two variables. A point represents each individual or object, and an association between two variables can be studied by analyzing patterns across multiple points. A regression line is added to a graph to determine whether the association between two variables can be explained or not. Fig. 2 illustrates correlations between pain scoring systems that are currently used (PSQ, Pain Sensitivity Questionnaire; PASS, Pain Anxiety Symptoms Scale; PCS, Pain Catastrophizing Scale) and Geop-Pain Questionnaire (GPQ) with the correlation coefficient, R, and regression line indicated on the scatter plot [ 6 ]. If multiple points exist at an identical location as in this example ( Fig. 2 ), the correlation level may not be clear. In this case, a correlation coefficient or regression line can be added to further elucidate the correlation.

Bar graph and histogram

A bar graph is used to indicate and compare values in a discrete category or group, and the frequency or other measurement parameters (i.e. mean). Depending on the number of categories, and the size or complexity of each category, bars may be created vertically or horizontally. The height (or length) of a bar represents the amount of information in a category. Bar graphs are flexible, and can be used in a grouped or subdivided bar format in cases of two or more data sets in each category. Fig. 3 is a representative example of a vertical bar graph, with the x -axis representing the length of recovery room stay and drug-treated group, and the y -axis representing the visual analog scale (VAS) score. The mean and standard deviation of the VAS scores are expressed as whiskers on the bars ( Fig. 3 ) [ 7 ].

By comparing the endpoints of bars, one can identify the largest and the smallest categories, and understand gradual differences between each category. It is advised to start the x - and y -axes from 0. Illustration of comparison results in the x - and y -axes that do not start from 0 can deceive readers' eyes and lead to overrepresentation of the results.

One form of vertical bar graph is the stacked vertical bar graph. A stack vertical bar graph is used to compare the sum of each category, and analyze parts of a category. While stacked vertical bar graphs are excellent from the aspect of visualization, they do not have a reference line, making comparison of parts of various categories challenging ( Fig. 4 ) [ 8 ].

A pie chart, which is used to represent nominal data (in other words, data classified in different categories), visually represents a distribution of categories. It is generally the most appropriate format for representing information grouped into a small number of categories. It is also used for data that have no other way of being represented aside from a table (i.e. frequency table). Fig. 5 illustrates the distribution of regular waste from operation rooms by their weight [ 8 ]. A pie chart is also commonly used to illustrate the number of votes each candidate won in an election.

Line plot with whiskers

A line plot is useful for representing time-series data such as monthly precipitation and yearly unemployment rates; in other words, it is used to study variables that are observed over time. Line graphs are especially useful for studying patterns and trends across data that include climatic influence, large changes or turning points, and are also appropriate for representing not only time-series data, but also data measured over the progression of a continuous variable such as distance. As can be seen in Fig. 1 , mean and standard deviation of systolic blood pressure are indicated for each time point, which enables readers to easily understand changes of systolic pressure over time [ 1 ]. If data are collected at a regular interval, values in between the measurements can be estimated. In a line graph, the x-axis represents the continuous variable, while the y-axis represents the scale and measurement values. It is also useful to represent multiple data sets on a single line graph to compare and analyze patterns across different data sets.

Box and whisker chart

A box and whisker chart does not make any assumptions about the underlying statistical distribution, and represents variations in samples of a population; therefore, it is appropriate for representing nonparametric data. AA box and whisker chart consists of boxes that represent interquartile range (one to three), the median and the mean of the data, and whiskers presented as lines outside of the boxes. Whiskers can be used to present the largest and smallest values in a set of data or only a part of the data (i.e. 95% of all the data). Data that are excluded from the data set are presented as individual points and are called outliers. The spacing at both ends of the box indicates dispersion in the data. The relative location of the median demonstrated within the box indicates skewness ( Fig. 6 ). The box and whisker chart provided as an example represents calculated volumes of an anesthetic, desflurane, consumed over the course of the observation period ( Fig. 7 ) [ 9 ].

Three-dimensional effects

Most of the recently introduced statistical packages and graphics software have the three-dimensional (3D) effect feature. The 3D effects can add depth and perspective to a graph. However, since they may make reading and interpreting data more difficult, they must only be used after careful consideration. The application of 3D effects on a pie chart makes distinguishing the size of each slice difficult. Even if slices are of similar sizes, slices farther from the front of the pie chart may appear smaller than the slices closer to the front ( Fig. 8 ).

Drawing a graph: example

Finally, we explain how to create a graph by using a line graph as an example ( Fig. 9 ). In Fig. 9 , the mean values of arterial pressure were randomly produced and assumed to have been measured on an hourly basis. In many graphs, the x- and y-axes meet at the zero point ( Fig. 9A ). In this case, information regarding the mean and standard deviation of mean arterial pressure measurements corresponding to t = 0 cannot be conveyed as the values overlap with the y-axis. The data can be clearly exposed by separating the zero point ( Fig. 9B ). In Fig. 9B , the mean and standard deviation of different groups overlap and cannot be clearly distinguished from each other. Separating the data sets and presenting standard deviations in a single direction prevents overlapping and, therefore, reduces the visual inconvenience. Doing so also reduces the excessive number of ticks on the y-axis, increasing the legibility of the graph ( Fig. 9C ). In the last graph, different shapes were used for the lines connecting different time points to further allow the data to be distinguished, and the y-axis was shortened to get rid of the unnecessary empty space present in the previous graphs ( Fig. 9D ). A graph can be made easier to interpret by assigning each group to a different color, changing the shape of a point, or including graphs of different formats [ 10 ]. The use of random settings for the scale in a graph may lead to inappropriate presentation or presentation of data that can deceive readers' eyes ( Fig. 10 ).

Owing to the lack of space, we could not discuss all types of graphs, but have focused on describing graphs that are frequently used in scholarly articles. We have summarized the commonly used types of graphs according to the method of data analysis in Table 3 . For general guidelines on graph designs, please refer to the journal submission requirements 2) .

Conclusions

Text, tables, and graphs are effective communication media that present and convey data and information. They aid readers in understanding the content of research, sustain their interest, and effectively present large quantities of complex information. As journal editors and reviewers will scan through these presentations before reading the entire text, their importance cannot be disregarded. For this reason, authors must pay as close attention to selecting appropriate methods of data presentation as when they were collecting data of good quality and analyzing them. In addition, having a well-established understanding of different methods of data presentation and their appropriate use will enable one to develop the ability to recognize and interpret inappropriately presented data or data presented in such a way that it deceives readers' eyes [ 11 ].

<Appendix>

Output for presentation.

Discovery and communication are the two objectives of data visualization. In the discovery phase, various types of graphs must be tried to understand the rough and overall information the data are conveying. The communication phase is focused on presenting the discovered information in a summarized form. During this phase, it is necessary to polish images including graphs, pictures, and videos, and consider the fact that the images may look different when printed than how appear on a computer screen. In this appendix, we discuss important concepts that one must be familiar with to print graphs appropriately.

The KJA asks that pictures and images meet the following requirement before submission 3)

“Figures and photographs should be submitted as ‘TIFF’ files. Submit files of figures and photographs separately from the text of the paper. Width of figure should be 84 mm (one column). Contrast of photos or graphs should be at least 600 dpi. Contrast of line drawings should be at least 1,200 dpi. The Powerpoint file (ppt, pptx) is also acceptable.”

Unfortunately, without sufficient knowledge of computer graphics, it is not easy to understand the submission requirement above. Therefore, it is necessary to develop an understanding of image resolution, image format (bitmap and vector images), and the corresponding file specifications.

Resolution is often mentioned to describe the quality of images containing graphs or CT/MRI scans, and video files. The higher the resolution, the clearer and closer to reality the image is, while the opposite is true for low resolutions. The most representative unit used to describe a resolution is “dpi” (dots per inch): this literally translates to the number of dots required to constitute 1 inch. The greater the number of dots, the higher the resolution. The KJA submission requirements recommend 600 dpi for images, and 1,200 dpi 4) for graphs. In other words, resolutions in which 600 or 1,200 dots constitute one inch are required for submission.

There are requirements for the horizontal length of an image in addition to the resolution requirements. While there are no requirements for the vertical length of an image, it must not exceed the vertical length of a page. The width of a column on one side of a printed page is 84 mm, or 3.3 inches (84/25.4 mm ≒ 3.3 inches). Therefore, a graph must have a resolution in which 1,200 dots constitute 1 inch, and have a width of 3.3 inches.

Bitmap and Vector

Methods of image construction are important. Bitmap images can be considered as images drawn on section paper. Enlarging the image will enlarge the picture along with the grid, resulting in a lower resolution; in other words, aliasing occurs. On the other hand, reducing the size of the image will reduce the size of the picture, while increasing the resolution. In other words, resolution and the size of an image are inversely proportionate to one another in bitmap images, and it is a drawback of bitmap images that resolution must be considered when adjusting the size of an image. To enlarge an image while maintaining the same resolution, the size and resolution of the image must be determined before saving the image. An image that has already been created cannot avoid changes to its resolution according to changes in size. Enlarging an image while maintaining the same resolution will increase the number of horizontal and vertical dots, ultimately increasing the number of pixels 5) of the image, and the file size. In other words, the file size of a bitmap image is affected by the size and resolution of the image (file extensions include JPG [JPEG] 6) , PNG 7) , GIF 8) , and TIF [TIFF] 9) . To avoid this complexity, the width of an image can be set to 4 inches and its resolution to 900 dpi to satisfy the submission requirements of most journals [ 12 ].

Vector images overcome the shortcomings of bitmap images. Vector images are created based on mathematical operations of line segments and areas between different points, and are not affected by aliasing or pixelation. Furthermore, they result in a smaller file size that is not affected by the size of the image. They are commonly used for drawings and illustrations (file extensions include EPS 10) , CGM 11) , and SVG 12) ).

Finally, the PDF 13) is a file format developed by Adobe Systems (Adobe Systems, CA, USA) for electronic documents, and can contain general documents, text, drawings, images, and fonts. They can also contain bitmap and vector images. While vector images are used by researchers when working in Powerpoint, they are saved as 960 × 720 dots when saved in TIFF format in Powerpoint. This results in a resolution that is inappropriate for printing on a paper medium. To save high-resolution bitmap images, the image must be saved as a PDF file instead of a TIFF, and the saved PDF file must be imported into an imaging processing program such as Photoshop™(Adobe Systems, CA, USA) to be saved in TIFF format [ 12 ].

1) Instructions to authors in KJA; section 5-(9) Table; https://ekja.org/index.php?body=instruction

2) Instructions to Authors in KJA; section 6-1)-(10) Figures and illustrations in Manuscript preparation; https://ekja.org/index.php?body=instruction

3) Instructions to Authors in KJA; section 6-1)-(10) Figures and illustrations in Manuscript preparation; https://ekja.org/index.php?body=instruction

4) Resolution; in KJA, it is represented by “contrast.”

5) Pixel is a minimum unit of an image and contains information of a dot and color. It is derived by multiplying the number of vertical and horizontal dots regardless of image size. For example, Full High Definition (FHD) monitor has 1920 × 1080 dots ≒ 2.07 million pixel.

6) Joint Photographic Experts Group.

7) Portable Network Graphics.

8) Graphics Interchange Format

9) Tagged Image File Format; TIFF

10) Encapsulated PostScript.

11) Computer Graphics Metafile.

12) Scalable Vector Graphics.

13) Portable Document Format.

Presentation of Data

Statistics deals with the collection, presentation and analysis of the data, as well as drawing meaningful conclusions from the given data. Generally, the data can be classified into two different types, namely primary data and secondary data. If the information is collected by the investigator with a definite objective in their mind, then the data obtained is called the primary data. If the information is gathered from a source, which already had the information stored, then the data obtained is called secondary data. Once the data is collected, the presentation of data plays a major role in concluding the result. Here, we will discuss how to present the data with many solved examples.

What is Meant by Presentation of Data?

As soon as the data collection is over, the investigator needs to find a way of presenting the data in a meaningful, efficient and easily understood way to identify the main features of the data at a glance using a suitable presentation method. Generally, the data in the statistics can be presented in three different forms, such as textual method, tabular method and graphical method.

Presentation of Data Examples

Now, let us discuss how to present the data in a meaningful way with the help of examples.

Consider the marks given below, which are obtained by 10 students in Mathematics:

36, 55, 73, 95, 42, 60, 78, 25, 62, 75.

Find the range for the given data.

Given Data: 36, 55, 73, 95, 42, 60, 78, 25, 62, 75.

The data given is called the raw data.

First, arrange the data in the ascending order : 25, 36, 42, 55, 60, 62, 73, 75, 78, 95.

Therefore, the lowest mark is 25 and the highest mark is 95.

We know that the range of the data is the difference between the highest and the lowest value in the dataset.

Therefore, Range = 95-25 = 70.

Note: Presentation of data in ascending or descending order can be time-consuming if we have a larger number of observations in an experiment.

Now, let us discuss how to present the data if we have a comparatively more number of observations in an experiment.

Consider the marks obtained by 30 students in Mathematics subject (out of 100 marks)

10, 20, 36, 92, 95, 40, 50, 56, 60, 70, 92, 88, 80, 70, 72, 70, 36, 40, 36, 40, 92, 40, 50, 50, 56, 60, 70, 60, 60, 88.

In this example, the number of observations is larger compared to example 1. So, the presentation of data in ascending or descending order is a bit time-consuming. Hence, we can go for the method called ungrouped frequency distribution table or simply frequency distribution table . In this method, we can arrange the data in tabular form in terms of frequency.

For example, 3 students scored 50 marks. Hence, the frequency of 50 marks is 3. Now, let us construct the frequency distribution table for the given data.

Therefore, the presentation of data is given as below:

The following example shows the presentation of data for the larger number of observations in an experiment.

Consider the marks obtained by 100 students in a Mathematics subject (out of 100 marks)

95, 67, 28, 32, 65, 65, 69, 33, 98, 96,76, 42, 32, 38, 42, 40, 40, 69, 95, 92, 75, 83, 76, 83, 85, 62, 37, 65, 63, 42, 89, 65, 73, 81, 49, 52, 64, 76, 83, 92, 93, 68, 52, 79, 81, 83, 59, 82, 75, 82, 86, 90, 44, 62, 31, 36, 38, 42, 39, 83, 87, 56, 58, 23, 35, 76, 83, 85, 30, 68, 69, 83, 86, 43, 45, 39, 83, 75, 66, 83, 92, 75, 89, 66, 91, 27, 88, 89, 93, 42, 53, 69, 90, 55, 66, 49, 52, 83, 34, 36.

Now, we have 100 observations to present the data. In this case, we have more data when compared to example 1 and example 2. So, these data can be arranged in the tabular form called the grouped frequency table. Hence, we group the given data like 20-29, 30-39, 40-49, ….,90-99 (As our data is from 23 to 98). The grouping of data is called the “class interval” or “classes”, and the size of the class is called “class-size” or “class-width”.

In this case, the class size is 10. In each class, we have a lower-class limit and an upper-class limit. For example, if the class interval is 30-39, the lower-class limit is 30, and the upper-class limit is 39. Therefore, the least number in the class interval is called the lower-class limit and the greatest limit in the class interval is called upper-class limit.

Hence, the presentation of data in the grouped frequency table is given below:

Hence, the presentation of data in this form simplifies the data and it helps to enable the observer to understand the main feature of data at a glance.

Practice Problems

• The heights of 50 students (in cms) are given below. Present the data using the grouped frequency table by taking the class intervals as 160 -165, 165 -170, and so on.  Data: 161, 150, 154, 165, 168, 161, 154, 162, 150, 151, 162, 164, 171, 165, 158, 154, 156, 172, 160, 170, 153, 159, 161, 170, 162, 165, 166, 168, 165, 164, 154, 152, 153, 156, 158, 162, 160, 161, 173, 166, 161, 159, 162, 167, 168, 159, 158, 153, 154, 159.
• Three coins are tossed simultaneously and each time the number of heads occurring is noted and it is given below. Present the data using the frequency distribution table. Data: 0, 1, 2, 2, 1, 2, 3, 1, 3, 0, 1, 3, 1, 1, 2, 2, 0, 1, 2, 1, 3, 0, 0, 1, 1, 2, 3, 2, 2, 0.

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• Textual And Tabular Presentation Of Data

Think about a scenario where your report cards are printed in a textual format. Your grades and remarks about you are presented in a paragraph format instead of data tables. Would be very confusing right? This is why data must be presented correctly and clearly. Let us take a look.

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Presentation of data.

Presentation of data is of utter importance nowadays. Afterall everything that’s pleasing to our eyes never fails to grab our attention. Presentation of data refers to an exhibition or putting up data in an attractive and useful manner such that it can be easily interpreted. The three main forms of presentation of data are:

• Textual presentation
• Data tables
• Diagrammatic presentation

Here we will be studying only the textual and tabular presentation, i.e. data tables in some detail.

Textual Presentation

The discussion about the presentation of data starts off with it’s most raw and vague form which is the textual presentation. In such form of presentation, data is simply mentioned as mere text, that is generally in a paragraph. This is commonly used when the data is not very large.

This kind of representation is useful when we are looking to supplement qualitative statements with some data. For this purpose, the data should not be voluminously represented in tables or diagrams. It just has to be a statement that serves as a fitting evidence to our qualitative evidence and helps the reader to get an idea of the scale of a phenomenon .

For example, “the 2002 earthquake proved to be a mass murderer of humans . As many as 10,000 citizens have been reported dead”. The textual representation of data simply requires some intensive reading. This is because the quantitative statement just serves as an evidence of the qualitative statements and one has to go through the entire text before concluding anything.

Further, if the data under consideration is large then the text matter increases substantially. As a result, the reading process becomes more intensive, time-consuming and cumbersome.

Data Tables or Tabular Presentation

A table facilitates representation of even large amounts of data in an attractive, easy to read and organized manner. The data is organized in rows and columns. This is one of the most widely used forms of presentation of data since data tables are easy to construct and read.

Components of  Data Tables

• Table Number : Each table should have a specific table number for ease of access and locating. This number can be readily mentioned anywhere which serves as a reference and leads us directly to the data mentioned in that particular table.
• Title:  A table must contain a title that clearly tells the readers about the data it contains, time period of study, place of study and the nature of classification of data .
• Headnotes:  A headnote further aids in the purpose of a title and displays more information about the table. Generally, headnotes present the units of data in brackets at the end of a table title.
• Stubs:  These are titles of the rows in a table. Thus a stub display information about the data contained in a particular row.
• Caption:  A caption is the title of a column in the data table. In fact, it is a counterpart if a stub and indicates the information contained in a column.
• Body or field:  The body of a table is the content of a table in its entirety. Each item in a body is known as a ‘cell’.
• Footnotes:  Footnotes are rarely used. In effect, they supplement the title of a table if required.
• Source:  When using data obtained from a secondary source, this source has to be mentioned below the footnote.

Construction of Data Tables

There are many ways for construction of a good table. However, some basic ideas are:

• The title should be in accordance with the objective of study:  The title of a table should provide a quick insight into the table.
• Comparison:  If there might arise a need to compare any two rows or columns then these might be kept close to each other.
• Alternative location of stubs:  If the rows in a data table are lengthy, then the stubs can be placed on the right-hand side of the table.
• Headings:  Headings should be written in a singular form. For example, ‘good’ must be used instead of ‘goods’.
• Footnote:  A footnote should be given only if needed.
• Size of columns:  Size of columns must be uniform and symmetrical.
• Use of abbreviations:  Headings and sub-headings should be free of abbreviations.
• Units: There should be a clear specification of units above the columns.

The Advantages of Tabular Presentation

• Ease of representation:  A large amount of data can be easily confined in a data table. Evidently, it is the simplest form of data presentation.
• Ease of analysis:  Data tables are frequently used for statistical analysis like calculation of central tendency, dispersion etc.
• Helps in comparison:  In a data table, the rows and columns which are required to be compared can be placed next to each other. To point out, this facilitates comparison as it becomes easy to compare each value.
• Economical:  Construction of a data table is fairly easy and presents the data in a manner which is really easy on the eyes of a reader. Moreover, it saves time as well as space.

Classification of Data and Tabular Presentation

Qualitative classification.

In this classification, data in a table is classified on the basis of qualitative attributes. In other words, if the data contained attributes that cannot be quantified like rural-urban, boys-girls etc. it can be identified as a qualitative classification of data.

Quantitative Classification

In quantitative classification, data is classified on basis of quantitative attributes.

Temporal Classification

Here data is classified according to time. Thus when data is mentioned with respect to different time frames, we term such a classification as temporal.

Spatial Classification

When data is classified according to a location, it becomes a spatial classification.

A Solved Example for You

Q:  The classification in which data in a table is classified according to time is known as:

• Qualitative
• Quantitative

Ans:  The form of classification in which data is classified based on time frames is known as the temporal classification of data and tabular presentation.

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• Diagrammatic Presentation of Data

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Data presentation: A comprehensive guide

Learn how to create data presentation effectively and communicate your insights in a way that is clear, concise, and engaging.

Raja Bothra

Building presentations

Hey there, fellow data enthusiast!

Welcome to our comprehensive guide on data presentation.

Whether you're an experienced presenter or just starting, this guide will help you present your data like a pro.

We'll dive deep into what data presentation is, why it's crucial, and how to master it. So, let's embark on this data-driven journey together.

What is data presentation?

Data presentation is the art of transforming raw data into a visual format that's easy to understand and interpret. It's like turning numbers and statistics into a captivating story that your audience can quickly grasp. When done right, data presentation can be a game-changer, enabling you to convey complex information effectively.

Why are data presentations important?

Imagine drowning in a sea of numbers and figures. That's how your audience might feel without proper data presentation. Here's why it's essential:

• Clarity : Data presentations make complex information clear and concise.
• Engagement : Visuals, such as charts and graphs, grab your audience's attention.
• Comprehension : Visual data is easier to understand than long, numerical reports.
• Decision-making : Well-presented data aids informed decision-making.
• Impact : It leaves a lasting impression on your audience.

Types of data presentation

Now, let's delve into the diverse array of data presentation methods, each with its own unique strengths and applications. We have three primary types of data presentation, and within these categories, numerous specific visualization techniques can be employed to effectively convey your data.

1. Textual presentation

Textual presentation harnesses the power of words and sentences to elucidate and contextualize your data. This method is commonly used to provide a narrative framework for the data, offering explanations, insights, and the broader implications of your findings. It serves as a foundation for a deeper understanding of the data's significance.

2. Tabular presentation

Tabular presentation employs tables to arrange and structure your data systematically. These tables are invaluable for comparing various data groups or illustrating how data evolves over time. They present information in a neat and organized format, facilitating straightforward comparisons and reference points.

3. Graphical presentation

Graphical presentation harnesses the visual impact of charts and graphs to breathe life into your data. Charts and graphs are powerful tools for spotlighting trends, patterns, and relationships hidden within the data. Let's explore some common graphical presentation methods:

• Bar charts: They are ideal for comparing different categories of data. In this method, each category is represented by a distinct bar, and the height of the bar corresponds to the value it represents. Bar charts provide a clear and intuitive way to discern differences between categories.
• Pie charts: It excel at illustrating the relative proportions of different data categories. Each category is depicted as a slice of the pie, with the size of each slice corresponding to the percentage of the total value it represents. Pie charts are particularly effective for showcasing the distribution of data.
• Line graphs: They are the go-to choice when showcasing how data evolves over time. Each point on the line represents a specific value at a particular time period. This method enables viewers to track trends and fluctuations effortlessly, making it perfect for visualizing data with temporal dimensions.
• Scatter plots: They are the tool of choice when exploring the relationship between two variables. In this method, each point on the plot represents a pair of values for the two variables in question. Scatter plots help identify correlations, outliers, and patterns within data pairs.

The selection of the most suitable data presentation method hinges on the specific dataset and the presentation's objectives. For instance, when comparing sales figures of different products, a bar chart shines in its simplicity and clarity. On the other hand, if your aim is to display how a product's sales have changed over time, a line graph provides the ideal visual narrative.

Additionally, it's crucial to factor in your audience's level of familiarity with data presentations. For a technical audience, more intricate visualization methods may be appropriate. However, when presenting to a general audience, opting for straightforward and easily understandable visuals is often the wisest choice.

In the world of data presentation, choosing the right method is akin to selecting the perfect brush for a masterpiece. Each tool has its place, and understanding when and how to use them is key to crafting compelling and insightful presentations. So, consider your data carefully, align your purpose, and paint a vivid picture that resonates with your audience.

What to include in data presentation

When creating your data presentation, remember these key components:

• Data points : Clearly state the data points you're presenting.
• Comparison : Highlight comparisons and trends in your data.
• Graphical methods : Choose the right chart or graph for your data.
• Infographics : Use visuals like infographics to make information more digestible.
• Numerical values : Include numerical values to support your visuals.
• Qualitative information : Explain the significance of the data.
• Source citation : Always cite your data sources.

How to structure an effective data presentation

Creating a well-structured data presentation is not just important; it's the backbone of a successful presentation. Here's a step-by-step guide to help you craft a compelling and organized presentation that captivates your audience:

1. Know your audience

Understanding your audience is paramount. Consider their needs, interests, and existing knowledge about your topic. Tailor your presentation to their level of understanding, ensuring that it resonates with them on a personal level. Relevance is the key.

2. Have a clear message

Every effective data presentation should convey a clear and concise message. Determine what you want your audience to learn or take away from your presentation, and make sure your message is the guiding light throughout your presentation. Ensure that all your data points align with and support this central message.

3. Tell a compelling story

Human beings are naturally wired to remember stories. Incorporate storytelling techniques into your presentation to make your data more relatable and memorable. Your data can be the backbone of a captivating narrative, whether it's about a trend, a problem, or a solution. Take your audience on a journey through your data.

4. Leverage visuals

Visuals are a powerful tool in data presentation. They make complex information accessible and engaging. Utilize charts, graphs, and images to illustrate your points and enhance the visual appeal of your presentation. Visuals should not just be an accessory; they should be an integral part of your storytelling.

5. Be clear and concise

Avoid jargon or technical language that your audience may not comprehend. Use plain language and explain your data points clearly. Remember, clarity is king. Each piece of information should be easy for your audience to digest.

6. Practice your delivery

Practice makes perfect. Rehearse your presentation multiple times before the actual delivery. This will help you deliver it smoothly and confidently, reducing the chances of stumbling over your words or losing track of your message.

A basic structure for an effective data presentation

Armed with a comprehensive comprehension of how to construct a compelling data presentation, you can now utilize this fundamental template for guidance:

In the introduction, initiate your presentation by introducing both yourself and the topic at hand. Clearly articulate your main message or the fundamental concept you intend to communicate.

Moving on to the body of your presentation, organize your data in a coherent and easily understandable sequence. Employ visuals generously to elucidate your points and weave a narrative that enhances the overall story. Ensure that the arrangement of your data aligns with and reinforces your central message.

As you approach the conclusion, succinctly recapitulate your key points and emphasize your core message once more. Conclude by leaving your audience with a distinct and memorable takeaway, ensuring that your presentation has a lasting impact.

Additional tips for enhancing your data presentation

To take your data presentation to the next level, consider these additional tips:

• Consistent design : Maintain a uniform design throughout your presentation. This not only enhances visual appeal but also aids in seamless comprehension.
• High-quality visuals : Ensure that your visuals are of high quality, easy to read, and directly relevant to your topic.
• Concise text : Avoid overwhelming your slides with excessive text. Focus on the most critical points, using visuals to support and elaborate.
• Anticipate questions : Think ahead about the questions your audience might pose. Be prepared with well-thought-out answers to foster productive discussions.

By following these guidelines, you can structure an effective data presentation that not only informs but also engages and inspires your audience. Remember, a well-structured presentation is the bridge that connects your data to your audience's understanding and appreciation.

Do’s and don'ts on a data presentation

• Use visuals : Incorporate charts and graphs to enhance understanding.
• Keep it simple : Avoid clutter and complexity.
• Highlight key points : Emphasize crucial data.
• Engage the audience : Encourage questions and discussions.
• Practice : Rehearse your presentation.

Don'ts:

• Overload with data : Less is often more; don't overwhelm your audience.
• Fit Unrelated data : Stay on topic; don't include irrelevant information.
• Neglect the audience : Ensure your presentation suits your audience's level of expertise.
• Read word-for-word : Avoid reading directly from slides.
• Lose focus : Stick to your presentation's purpose.

Summarizing key takeaways

• Definition : Data presentation is the art of visualizing complex data for better understanding.
• Importance : Data presentations enhance clarity, engage the audience, aid decision-making, and leave a lasting impact.
• Types : Textual, Tabular, and Graphical presentations offer various ways to present data.
• Choosing methods : Select the right method based on data, audience, and purpose.
• Components : Include data points, comparisons, visuals, infographics, numerical values, and source citations.
• Structure : Know your audience, have a clear message, tell a compelling story, use visuals, be concise, and practice.
• Do's and don'ts : Do use visuals, keep it simple, highlight key points, engage the audience, and practice. Don't overload with data, include unrelated information, neglect the audience's expertise, read word-for-word, or lose focus.

1. What is data presentation, and why is it important in 2023?

Data presentation is the process of visually representing data sets to convey information effectively to an audience. In an era where the amount of data generated is vast, visually presenting data using methods such as diagrams, graphs, and charts has become crucial. By simplifying complex data sets, presentation of the data may helps your audience quickly grasp much information without drowning in a sea of chart's, analytics, facts and figures.

2. What are some common methods of data presentation?

There are various methods of data presentation, including graphs and charts, histograms, and cumulative frequency polygons. Each method has its strengths and is often used depending on the type of data you're using and the message you want to convey. For instance, if you want to show data over time, try using a line graph. If you're presenting geographical data, consider to use a heat map.

3. How can I ensure that my data presentation is clear and readable?

To ensure that your data presentation is clear and readable, pay attention to the design and labeling of your charts. Don't forget to label the axes appropriately, as they are critical for understanding the values they represent. Don't fit all the information in one slide or in a single paragraph. Presentation software like Prezent and PowerPoint can help you simplify your vertical axis, charts and tables, making them much easier to understand.

4. What are some common mistakes presenters make when presenting data?

One common mistake is trying to fit too much data into a single chart, which can distort the information and confuse the audience. Another mistake is not considering the needs of the audience. Remember that your audience won't have the same level of familiarity with the data as you do, so it's essential to present the data effectively and respond to questions during a Q&A session.

5. How can I use data visualization to present important data effectively on platforms like LinkedIn?

When presenting data on platforms like LinkedIn, consider using eye-catching visuals like bar graphs or charts. Use concise captions and e.g., examples to highlight the single most important information in your data report. Visuals, such as graphs and tables, can help you stand out in the sea of textual content, making your data presentation more engaging and shareable among your LinkedIn connections.

Create your data presentation with prezent

Prezent can be a valuable tool for creating data presentations. Here's how Prezent can help you in this regard:

• Time savings : Prezent saves up to 70% of presentation creation time, allowing you to focus on data analysis and insights.
• On-brand consistency : Ensure 100% brand alignment with Prezent's brand-approved designs for professional-looking data presentations.
• Effortless collaboration : Real-time sharing and collaboration features make it easy for teams to work together on data presentations.
• Data storytelling : Choose from 50+ storylines to effectively communicate data insights and engage your audience.
• Personalization : Create tailored data presentations that resonate with your audience's preferences, enhancing the impact of your data.

In summary, Prezent streamlines the process of creating data presentations by offering time-saving features, ensuring brand consistency, promoting collaboration, and providing tools for effective data storytelling. Whether you need to present data to clients, stakeholders, or within your organization, Prezent can significantly enhance your presentation-making process.

So, go ahead, present your data with confidence, and watch your audience be wowed by your expertise.

Thank you for joining us on this data-driven journey. Stay tuned for more insights, and remember, data presentation is your ticket to making numbers come alive!

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TEXTUAL, TABULAR & DIAGRAMMATIC PRESENTATION OF DATA

STATISTICS : PRESENTATION OF DATA

Data can be presented in three ways:

• Textual presentation
• Tabular presentation
• Diagrammatic presentation

1. Textual Mode of presentation is  layman’s method of presentation of data.  Anyone can prepare, anyone can understand. No specific skill(s) is/are required.

2. Tabular Mode of presentation is  the most accurate mode of presentation of data.  It requires a lot of skill to prepare, and some skill(s) to understand. Table facilitates comparison.

But, Table should be good enough as per some points of view:

• 1. Appealing
• 2. Well-balanced
• 3. Compulsory Title and Table Number
• 4. Title should be  self-explanatory
• 5. Units must be properly mentioned
• 6. Comparison should be easy
• 7. Sources and footnotes (if any) must be mentioned at the bottom

Below is a sample of how a table should look like:

Table No. 1: Format of a table

* Sources: 1. Kailasha Foundation – Fun & Learn Portal LMS Directory *Footnotes: The entire upper part of the table is called BOX HEAD.

3. Diagrammatic Mode of Presentation:

A. Non-Frequency Diagrams: Non-frequency diagrams correspond to the data  which are NOT frequency data.  (a) Bar Diagrams (b) Line Diagrams (Historiagram) (c) Pie Diagram or Pie Chart

B. Frequency Diagrams: Frequency Data are presented. Mostly class-intervals are presented via this mode. Three most common frequency diagrams are: (a) Histogram (b) Frequency Polygon (c) Ogives: (i) Less than type Ogives (ii) More than type Ogives

• 1. Bar Diagram and Line Diagram are inter-convertible
• 2. Bar Diagram and Line Diagram can both be of simple and multiple types
• 3. Multiple bar diagram or Multiple Line diagram is used when two related series (in same unit) are to be compared
• 4. Multiple axis bar diagram or Multiple axis Line diagram is used when units in the two series are different

ILLUSTRATIONS OF PRESENTATION OF DATA:

Bar Diagrams:

Line Diagram:

Multiple  Bar Diagram:

Frequency Polygon:

FREQUENCY CURVE:

A smooth join of all vertices of a frequency polygon. This is broadly divided into four shapes:

(i) Bell Shaped (Most Common Shape) (ii) U-Shaped (iii) J – Shaped: Simple J – shaped & Inverted J – Shaped (iv) Mixed Curve (Second Most Common Shape)

• 1. CENSUS: The collection of data from every element in a population or universe or arena of statistical enquiry.
• 2. SAMPLE: The collection of data from subgroup or subset of the population.
• 3. FREQUENCY: The number of times a certain value or class of values occurs.
• 4. CUMULATIVE FREQUENCY: The running total of the frequencies at each class interval level.
• 5. FREQUENCY DISTRIBUTION: The organization of raw data in table form with classes and frequencies.
• 6. CLASS LIMITS: The  originally assigned extreme values  of classes are called class limits, viz. Lower class limit and upper class limit.
• 7. CLASS WIDTH: The difference between the upper and lower boundaries  (NOT limits) of any class.
• 8. CLASS BOUNDARY: After making the distribution continuous, the upper class boundary of a class becomes equal to the lower class boundary of the next class.
• 9. CLASS MARK: The mid-point of any class is called the class mark.

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Hindi explanation:.

ENGLISH EXPLANATION:

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Data Presentation

Josée Dupuis, PhD, Professor of Biostatistics, Boston University School of Public Health

Wayne LaMorte, MD, PhD, MPH, Professor of Epidemiology, Boston University School of Public Health

Introduction

While graphical summaries of data can certainly be powerful ways of communicating results clearly and unambiguously in a way that facilitates our ability to think about the information, poorly designed graphical displays can be ambiguous, confusing, and downright misleading. The keys to excellence in graphical design and communication are much like the keys to good writing. Adhere to fundamental principles of style and communicate as logically, accurately, and clearly as possible. Excellence in writing is generally achieved by avoiding unnecessary words and paragraphs; it is efficient. In a similar fashion, excellence in graphical presentation is generally achieved by efficient designs that avoid unnecessary ink.

Excellence in graphical presentation depends on:

• Choosing the best medium for presenting the information
• Designing the components of the graph in a way that communicates the information as clearly and accurately as possible.

Table or Graph?

• Tables are generally best if you want to be able to look up specific information or if the values must be reported precisely.
• Graphics are best for illustrating trends and making comparisons

The side by side illustrations below show the same information, first in table form and then in graphical form. While the information in the table is precise, the real goal is to compare a series of clinical outcomes in subjects taking either a drug or a placebo. The graphical presentation on the right makes it possible to quickly see that for each of the outcomes evaluated, the drug produced relief in a great proportion of subjects. Moreover, the viewer gets a clear sense of the magnitude of improvement, and the error bars provided a sense of the uncertainty in the data.

Principles for Table Display

• Sort table rows in a meaningful way
• Avoid alphabetical listing!
• Use rates, proportions or ratios in addition (or instead of) totals
• Show more than two time points if available
• Multiple time points may be better presented in a Figure
• Similar data should go down columns
• Highlight important comparisons
• Show the source of the data

Consider the data in the table below from http://www.cancer.gov/cancertopics/types/commoncancers

Our ability to quickly understand the relative frequency of these cancers is hampered by presenting them in alphabetical order. It is much easier for the reader to grasp the relative frequency by listing them from most frequent to least frequent as in the next table.

However, the same information might be presented more effectively with a dot plot, as shown below.

Data from http://www.cancer.gov/cancertopics/types/commoncancers

Principles of Graphical Excellence from E.R. Tufte

Pattern perception.

Pattern perception is done by

• Detection: recognition of geometry encoding physical values
• Assembly: grouping of detected symbol elements; discerning overall patterns in data
• Estimation: assessment of relative magnitudes of two physical values

Geographic Variation in Cancer

As an example, Tufte offers a series of maps that summarize the age-adjusted mortality rates for various types of cancer in the 3,056 counties in the United States. The maps showing the geographic variation in stomach cancer are shown below.

These maps summarize an enormous amount of information and present it efficiently, coherently, and effectively.in a way that invites the viewer to make comparisons and to think about the substance of the findings. Consider, for example, that the region to the west of the Great Lakes was settled largely by immigrants from Germany and Scand anavia, where traditional methods of preserving food included pickling and curing of fish by smoking. Could these methods be associated with an increased risk of stomach cancer?

John Snow's Spot Map of Cholera Cases

Consider also the spot map that John Snow presented after the cholera outbreak in the Broad Street section of London in September 1854. Snow ascertained the place of residence or work of the victims and represented them on a map of the area using a small black disk to represent each victim and stacking them when more than one occurred at a particular location. Snow reasoned that cholera was probably caused by something that was ingested, because of the intense diarrhea and vomiting of the victims, and he noted that the vast majority of cholera deaths occurred in people who lived or worked in the immediate vicinity of the broad street pump (shown with a red dot that we added for clarity). He further ascertained that most of the victims drank water from the Broad Street pump, and it was this evidence that persuaded the authorities to remove the handle from the pump in order to prevent more deaths.

Humans can readily perceive differences like this when presented effectively as in the two previous examples. However, humans are not good at estimating differences without directly seeing them (especially for steep curves), and we are particularly bad at perceiving relative angles (the principal perception task used in a pie chart).

The use of pie charts is generally discouraged. Consider the pie chart on the left below. It is difficult to accurately assess the relative size of the components in the pie chart, because the human eye has difficulty judging angles. The dot plot on the right shows the same data, but it is much easier to quickly assess the relative size of the components and how they changed from Fiscal Year 2000 to Fiscal Year 2007.

Consider the information in the two pie charts below (showing the same information).The 3-dimensional pie chart on the left distorts the relative proportions. In contrast the 2-dimensional pie chart on the right makes it much easier to compare the relative size of the varies components..

More Principles of Graphical Excellence

Exclude unneeded dimensions.

These 3-dimensional techniques distort the data and actually interfere with our ability to make accurate comparisons. The distortion caused by 3-dimensional elements can be particularly severe when the graphic is slanted at an angle or when the viewer tends to compare ends up unwittingly comparing the areas of the ink rather than the heights of the bars.

It is much easier to make comparisons with a chart like the one below.

Source: Huang, C, Guo C, Nichols C, Chen S, Martorell R. Elevated levels of protein in urine in adulthood after exposure to

the Chinese famine of 1959–61 during gestation and the early postnatal period. Int. J. Epidemiol. (2014) 43 (6): 1806-1814 .

Omit "Chart Junk"

Consider these two examples.

Here is a simple enumeration of the number of pets in a neighborhood. There is absolutely no reason to connect these counts with lines. This is, in fact, confusing and inappropriate and nothing more than "chart junk."

Source: http://www.go-education.com/free-graph-maker.html

Moiré Vibration

Moiré effects are sometimes used in modern art to produce the appearance of vibration and movement. However, when these effects are applied to statistical presentations, they are distracting and add clutter because the visual noise interferes with the interpretation of the data.

Tufte presents the example shown below from Instituto de Expansao Commercial, Brasil, Graphicos Estatisticas (Rio de Janeiro, 1929, p. 15).

 While the intention is to present quantitative information about the textile industry, the moiré effects do not add anything, and they are distracting, if not visually annoying.

Present Data to Facilitate Comparisons

Here is an attempt to compare catches of cod fish and crab across regions and to relate the variation to changes in water temperature. The problem here is that the Y-axes are vastly different, making it hard to sort out what's really going on. Even the Y-axes for temperature are vastly different.

http://seananderson.ca/courses/11-multipanel/multipanel.pdf1

The ability to make comparisons is greatly facilitated by using the same scales for axes, as illustrated below.

Data source: Dawber TR, Meadors GF, Moore FE Jr. Epidemiological approaches to heart disease:

the Framingham Study. Am J Public Health Nations Health. 1951;41(3):279-81. PMID: 14819398

It is also important to avoid distorting the X-axis. Note in the example below that the space between 0.05 to 0.1 is the same as space between 0.1 and 0.2.

Source: Park JH, Gail MH, Weinberg CR, et al. Distribution of allele frequencies and effect sizes and

their interrelationships for common genetic susceptibility variants. Proc Natl Acad Sci U S A. 2011; 108:18026-31.

Consider the range of the Y-axis. In the examples below there is no relevant information below $40,000, so it is not necessary to begin the Y-axis at 0. The graph on the right makes more sense.

Also, consider using a log scale. this can be particularly useful when presenting ratios as in the example below.

Source: Broman KW, Murray JC, Sheffield VC, White RL, Weber JL (1998) Comprehensive human genetic maps:

Individual and sex-specific variation in recombination. American Journal of Human Genetics 63:861-869, Figure 1

We noted earlier that pie charts make it difficult to see differences within a single pie chart, but this is particularly difficult when data is presented with multiple pie charts, as in the example below.

Source: Bell ML, et al. (2007) Spatial and temporal variation in PM2.5 chemical composition in the United States

for health effects studies. Environmental Health Perspectives 115:989-995, Figure 3

When multiple comparisons are being made, it is essential to use colors and symbols in a consistent way, as in this example.

Source: Manning AK, LaValley M, Liu CT, et al.  Meta-Analysis of Gene-Environment Interaction:

Joint Estimation of SNP and SNP x Environment Regression Coefficients.  Genet Epidemiol 2011, 35(1):11-8.

Avoid putting too many lines on the same chart. In the example below, the only thing that is readily apparent is that 1980 was a very hot summer.

Data from National Weather Service Weather Forecast Office at

http://www.srh.noaa.gov/tsa/?n=climo_tulyeartemp

Make Efficient Use of Space

Reduce the ratio of ink to information.

This isn't efficient, because this graphic is totally uninformative.

Source: Mykland P, Tierney L, Yu B (1995) Regeneration in Markov chain samplers.  Journal of the American Statistical Association 90:233-241, Figure 1

Bar graphs add ink without conveying any additional information, and they are distracting. The graph below on the left inappropriately uses bars which clutter the graph without adding anything. The graph on the right displays the same data, by does so more clearly and with less clutter.

Multiple Types of Information on the Same Figure

Choosing the best graph type, bar charts, error bars and dot plots.

As noted previously, bar charts can be problematic. Here is another one presenting means and error bars, but the error bars are misleading because they only extend in one direction. A better alternative would have been to to use full error bars with a scatter plot, as illustrated previously (right).

Consider the four graphs below presenting the incidence of cancer by type. The upper left graph unnecessary uses bars, which take up a lot of ink. This layout also ends up making the fonts for the types of cancer too small. Small font is also a problem for the dot plot at the upper right, and this one also has unnecessary grid lines across the entire width.

The graph at the lower left has more readable labels and uses a simple dot plot, but the rank order is difficult to figure out.

The graph at the lower right is clearly the best, since the labels are readable, the magnitude of incidence is shown clearly by the dot plots, and the cancers are sorted by frequency.

Single Continuous Numeric Variable

In this situation a cumulative distribution function conveys the most information and requires no grouping of the variable. A box plot will show selected quantiles effectively, and box plots are especially useful when stratifying by multiple categories of another variable.

Histograms are also possible. Consider the examples below.

Two Variables

 The two graphs below summarize BMI (Body Mass Index) measurements in four categories, i.e., younger and older men and women. The graph on the left shows the means and 95% confidence interval for the mean in each of the four groups. This is easy to interpret, but the viewer cannot see that the data is actually quite skewed. The graph on the right shows the same information presented as a box plot. With this presentation method one gets a better understanding of the skewed distribution and how the groups compare.

The next example is a scatter plot with a superimposed smoothed line of prediction. The shaded region embracing the blue line is a representation of the 95% confidence limits for the estimated prediction. This was created using "ggplot" in the R programming language.

Source: Frank E. Harrell Jr. on graphics:  http://biostat.mc.vanderbilt.edu/twiki/pub/Main/StatGraphCourse/graphscourse.pdf (page 121)

Multivariate Data

The example below shows the use of multiple panels.

Source: Cleveland S. The Elements of Graphing Data. Hobart Press, Summit, NJ, 1994.

Displaying Uncertainty

• Error bars showing confidence limits
• Confidence bands drawn using two lines
• Shaded confidence bands
• Bayesian credible intervals
• Bayesian posterior densities

Confidence Limits

Shaded Confidence Bands

Source: Frank E. Harrell Jr. on graphics:  http://biostat.mc.vanderbilt.edu/twiki/pub/Main/StatGraphCourse/graphscourse.pdf

Source: Tweedie RL and Mengersen KL. (1992) Br. J. Cancer 66: 700-705

Forest Plot

This is a Forest plot summarizing 26 studies of cigarette smoke exposure on risk of lung cancer. The sizes of the black boxes indicating the estimated odds ratio are proportional to the sample size in each study.

Data from Tweedie RL and Mengersen KL. (1992) Br. J. Cancer 66: 700-705

Summary Recommendations

• In general, avoid bar plots
• Avoid chart junk and the use of too much ink relative to the information you are displaying. Keep it simple and clear.
• Avoid pie charts, because humans have difficulty perceiving relative angles.
• Pay attention to scale, and make scales consistent.
• Explore several ways to display the data!

12 Tips on How to Display Data Badly

Adapted from Wainer H.  How to Display Data Badly.  The American Statistician 1984; 38: 137-147. 

• Show as few data as possible
• Hide what data you do show; minimize the data-ink ratio
• Ignore the visual metaphor altogether
• Only order matters
• Graph data out of context
• Change scales in mid-axis
• Emphasize the trivial;  ignore the important
• Jiggle the baseline
• Alphabetize everything.
• Make your labels illegible, incomplete, incorrect, and ambiguous.
• More is murkier: use a lot of decimal places and make your graphs three dimensional whenever possible.
• If it has been done well in the past, think of another way to do it

Additional Resources

• Stephen Few: Designing Effective Tables and Graphs. http://www.perceptualedge.com/images/Effective_Chart_Design.pdf
• Gary Klaas: Presenting Data: Tabular and graphic display of social indicators. Illinois State University, 2002. http://lilt.ilstu.edu/gmklass/pos138/datadisplay/sections/goodcharts.htm (Note: The web site will be discontinued to be replaced by the Just Plain Data Analysis site).

Question and Answer forum for K12 Students

Textual and Tabular Presentation of Data: Classification, Data Tables etc

The compilation of these Presentation of Data Notes makes students exam preparation simpler and organised.

Textual and Tabular Presentation of Data

Think about a scenario where your report cards are printed in a textual format. Your grades and remarks about you are presented in a paragraph format instead of data tables. Would be very confusing right? This is why data must be presented correctly and clearly. Let us take a look.

Presentation of Data

Presentation of data is of utter importance nowadays. After all, everything that’s pleasing to our eyes never fails to grab our attention. Presentation of data refers to an exhibition or putting up data in an attractive and useful manner such that it can be easily interpreted. The three main forms of presentation of data are:

• Textual presentation
• Data tables
• Diagrammatic presentation

Here we will be studying only the textual and tabular presentation, i.e. data tables in some detail.

Textual Presentation

The discussion about the presentation of data starts off with its most raw and vague form which is the textual presentation. In such a form of presentation, data is simply mentioned as mere text, which is generally in a paragraph. This is commonly used when the data is not very large.

This kind of representation is useful when we are looking to supplement qualitative statements with some data. For this purpose, the data should not be voluminously represented in tables or diagrams. It just has to be a statement that serves as fitting evidence to our qualitative evidence and helps the reader to get an idea of the scale of a phenomenon.

For example, “the 2002 earthquake proved to be a mass murderer of humans. As many as 10,000 citizens have been reported dead”. The textual representation of data simply requires some intensive reading. This is because the quantitative statement just serves as evidence of the qualitative statements and one has to go through the entire text before concluding anything.

Further, if the data under consideration is large then the text matter increases substantially. As a result, the reading process becomes more intensive, time-consuming, and cumbersome.

Data Tables or Tabular Presentation

A table facilitates the representation of even large amounts of data in an attractive, easy to read, and organized manner. The data is organized in rows and columns. This is one of the most widely used forms of presentation of data since data tables are easy to construct and read.

Components of Data Tables Table Number: Each table should have a specific table number for ease of access and locating. This number can be readily mentioned anywhere which serves as a reference and leads us directly to the data mentioned in that particular table.

Title: A table must contain a title that clearly tells the readers about the data it contains, time period of study, place of study, and the nature of the classification of data.

Headnotes: A headnote further aids in the purpose of a title and displays more information about the table. Generally, headnotes present the units of data in brackets at the end of a table title.

Stubs: These are titles of the rows in a table. Thus a stub display information about the data contained in a particular row.

Caption: A caption is the title of a column in the data table. In fact, it is a counterpart if a stub and indicates the information contained in a column.

Body or field: The body of a table is the content of a table in its entirety. Each item in a body is known as a ‘cell’.

Footnotes: Footnotes are rarely used. In effect, they supplement the title of a table if required.

Source: When using data obtained from a secondary source, this source has to be mentioned below the footnote.

Construction of Data Tables There are many ways to construct a good table. However, some basic ideas are:

The title should be in accordance with the objective of the study: The title of a table should provide a quick insight into the table.

Comparison: If there might arise a need to compare any two rows or columns then these might be kept close to each other.

Alternative location of stubs: If the rows in a data table are lengthy, then the stubs can be placed on the right-hand side of the table.

Headings: Headings should be written in a singular form. For example, ‘good’ must be used instead of ‘goods’.

Footnote: A footnote should be given only if needed.

Size of columns: Size of columns must be uniform and symmetrical.

Use of abbreviations: Headings and sub-headings should be free of abbreviations.

Units: There should be a clear specification of units above the columns.

The Advantages of Tabular Presentation Ease of representation: A large amount of data can be easily confined in a data table. Evidently, it is the simplest form of data presentation.

Ease of analysis: Data tables are frequently used for statistical analysis like calculation of central tendency, dispersion, etc.

Helps in comparison: In a data table, the rows and columns which are required to be compared can be placed next to each other. To point out, this facilitates comparison as it becomes easy to compare each value.

Economical: Construction of a data table is fairly easy and presents the data in a manner which is really easy in the eyes of a reader. Moreover, it saves time as well as space.

Classification of Data and Tabular Presentation

Qualitative Classification In this classification, data in a table is classified on the basis of qualitative attributes. In other words, if the data contained attributes that cannot be quantified like rural-urban, boys-girls, etc. it can be identified as a qualitative classification of data.

Quantitative Classification In quantitative classification, data is classified on basis of quantitative attributes.

Temporal Classification Here data is classified according to time. Thus when data is mentioned with respect to different time frames, we term such a classification as temporal.

Spatial Classification When data is classified according to a location, it becomes a spatial classification.

Question: The classification in which data in a table is classified according to time is known as: 1. Qualitative 2. Quantitative 3. Temporal 4. Spatial Answer: The form of classification in which data is classified based on time frames is known as the temporal classification of data and tabular presentation.

Presentation of Statistical Data

• First Online: 24 February 2016

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Data are collected often in raw form. These are then not useable unless summarized. The techniques of presentation in tabular and graphical forms are introduced. Some illustrations provided are real-world examples. Graphical presentations cover bar chart, pie chart, histogram, frequency polygon, pareto chart, frequency curve and line diagram.

• Presentation
• Table presentation
• Graph presentation
• Types of presentation

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Methodology

• Textual Analysis | Guide, 3 Approaches & Examples

Textual Analysis | Guide, 3 Approaches & Examples

Published on November 8, 2019 by Jack Caulfield . Revised on June 22, 2023.

Textual analysis is a broad term for various research methods used to describe, interpret and understand texts. All kinds of information can be gleaned from a text – from its literal meaning to the subtext, symbolism, assumptions, and values it reveals.

The methods used to conduct textual analysis depend on the field and the aims of the research. It often aims to connect the text to a broader social, political, cultural, or artistic context. Relatedly, it’s good to be careful of confirmation bias when conducting these sorts of analyses, grounding your observations in clear and plausible ways.

Table of contents

What is a text, textual analysis in cultural and media studies, textual analysis in the social sciences, textual analysis in literary studies, other interesting articles.

The term “text” is broader than it seems. A text can be a piece of writing, such as a book, an email, or a transcribed conversation. But in this context, a text can also be any object whose meaning and significance you want to interpret in depth: a film, an image, an artifact, even a place.

The methods you use to analyze a text will vary according to the type of object and the purpose of your analysis:

• Analysis of a short story might focus on the imagery, narrative perspective and structure of the text.
• To analyze a film, not only the dialogue but also the cinematography and use of sound could be relevant to the analysis.
• A building might be analyzed in terms of its architectural features and how it is navigated by visitors.
• You could analyze the rules of a game and what kind of behaviour they are designed to encourage in players.

While textual analysis is most commonly applied to written language, bear in mind how broad the term “text” is and how varied the methods involved can be.

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In the fields of cultural studies and media studies, textual analysis is a key component of research. Researchers in these fields take media and cultural objects – for example, music videos, social media content, billboard advertising – and treat them as texts to be analyzed.

Usually working within a particular theoretical framework (for example, using postcolonial theory, media theory, or semiotics), researchers seek to connect elements of their texts with issues in contemporary politics and culture. They might analyze many different aspects of the text:

• Word choice
• Design elements
• Location of the text
• Target audience
• Relationship with other texts

Textual analysis in this context is usually creative and qualitative in its approach. Researchers seek to illuminate something about the underlying politics or social context of the cultural object they’re investigating.

In the social sciences, textual analysis is often applied to texts such as interview transcripts and surveys , as well as to various types of media. Social scientists use textual data to draw empirical conclusions about social relations.

Textual analysis in the social sciences sometimes takes a more quantitative approach , where the features of texts are measured numerically. For example, a researcher might investigate how often certain words are repeated in social media posts, or which colors appear most prominently in advertisements for products targeted at different demographics.

Some common methods of analyzing texts in the social sciences include content analysis , thematic analysis , and discourse analysis .

Textual analysis is the most important method in literary studies. Almost all work in this field involves in-depth analysis of texts – in this context, usually novels, poems, stories or plays.

Because it deals with literary writing, this type of textual analysis places greater emphasis on the deliberately constructed elements of a text: for example, rhyme and meter in a poem, or narrative perspective in a novel. Researchers aim to understand and explain how these elements contribute to the text’s meaning.

However, literary analysis doesn’t just involve discovering the author’s intended meaning. It often also explores potentially unintended connections between different texts, asks what a text reveals about the context in which it was written, or seeks to analyze a classic text in a new and unexpected way.

Some well-known examples of literary analysis show the variety of approaches that can be taken:

• Eve Kosofky Sedgwick’s book Between Men analyzes Victorian literature in light of more contemporary perspectives on gender and sexuality.
• Roland Barthes’ S/Z provides an in-depth structural analysis of a short story by Balzac.
• Harold Bloom’s The Anxiety of Influence applies his own “influence theory” to an analysis of various classic poets.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Normal distribution
• Measures of central tendency
• Chi square tests
• Confidence interval
• Quartiles & Quantiles
• Cluster sampling
• Stratified sampling
• Thematic analysis
• Cohort study
• Peer review
• Ethnography

Research bias

• Implicit bias
• Cognitive bias
• Conformity bias
• Hawthorne effect
• Availability heuristic
• Attrition bias
• Social desirability bias

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1.1 Definitions of Statistics, Probability, and Key Terms

The science of statistics deals with the collection, analysis, interpretation, and presentation of data . We see and use data in our everyday lives.

Collaborative Exercise

In your classroom, try this exercise. Have class members write down the average time—in hours, to the nearest half-hour—they sleep per night. Your instructor will record the data. Then create a simple graph, called a dot plot, of the data. A dot plot consists of a number line and dots, or points, positioned above the number line. For example, consider the following data:

5, 5.5, 6, 6, 6, 6.5, 6.5, 6.5, 6.5, 7, 7, 8, 8, 9.

The dot plot for this data would be as follows:

Does your dot plot look the same as or different from the example? Why? If you did the same example in an English class with the same number of students, do you think the results would be the same? Why or why not?

Where do your data appear to cluster? How might you interpret the clustering?

The questions above ask you to analyze and interpret your data. With this example, you have begun your study of statistics.

In this course, you will learn how to organize and summarize data. Organizing and summarizing data is called descriptive statistics . Two ways to summarize data are by graphing and by using numbers, for example, finding an average. After you have studied probability and probability distributions, you will use formal methods for drawing conclusions from good data. The formal methods are called inferential statistics . Statistical inference uses probability to determine how confident we can be that our conclusions are correct.

Effective interpretation of data, or inference, is based on good procedures for producing data and thoughtful examination of the data. You will encounter what will seem to be too many mathematical formulas for interpreting data. The goal of statistics is not to perform numerous calculations using the formulas, but to gain an understanding of your data. The calculations can be done using a calculator or a computer. The understanding must come from you. If you can thoroughly grasp the basics of statistics, you can be more confident in the decisions you make in life.

Statistical Models

Statistics, like all other branches of mathematics, uses mathematical models to describe phenomena that occur in the real world. Some mathematical models are deterministic. These models can be used when one value is precisely determined from another value. Examples of deterministic models are the quadratic equations that describe the acceleration of a car from rest or the differential equations that describe the transfer of heat from a stove to a pot. These models are quite accurate and can be used to answer questions and make predictions with a high degree of precision. Space agencies, for example, use deterministic models to predict the exact amount of thrust that a rocket needs to break away from Earth’s gravity and achieve orbit.

However, life is not always precise. While scientists can predict to the minute the time that the sun will rise, they cannot say precisely where a hurricane will make landfall. Statistical models can be used to predict life’s more uncertain situations. These special forms of mathematical models or functions are based on the idea that one value affects another value. Some statistical models are mathematical functions that are more precise—one set of values can predict or determine another set of values. Or some statistical models are mathematical functions in which a set of values do not precisely determine other values. Statistical models are very useful because they can describe the probability or likelihood of an event occurring and provide alternative outcomes if the event does not occur. For example, weather forecasts are examples of statistical models. Meteorologists cannot predict tomorrow’s weather with certainty. However, they often use statistical models to tell you how likely it is to rain at any given time, and you can prepare yourself based on this probability.

Probability

Probability is a mathematical tool used to study randomness. It deals with the chance of an event occurring. For example, if you toss a fair coin four times, the outcomes may not be two heads and two tails. However, if you toss the same coin 4,000 times, the outcomes will be close to half heads and half tails. The expected theoretical probability of heads in any one toss is 1 2 1 2 or .5. Even though the outcomes of a few repetitions are uncertain, there is a regular pattern of outcomes when there are many repetitions. After reading about the English statistician Karl Pearson who tossed a coin 24,000 times with a result of 12,012 heads, one of the authors tossed a coin 2,000 times. The results were 996 heads. The fraction 996 2,000 996 2,000 is equal to .498 which is very close to .5, the expected probability.

The theory of probability began with the study of games of chance such as poker. Predictions take the form of probabilities. To predict the likelihood of an earthquake, of rain, or whether you will get an A in this course, we use probabilities. Doctors use probability to determine the chance of a vaccination causing the disease the vaccination is supposed to prevent. A stockbroker uses probability to determine the rate of return on a client's investments.

In statistics, we generally want to study a population . You can think of a population as a collection of persons, things, or objects under study. To study the population, we select a sample . The idea of sampling is to select a portion, or subset, of the larger population and study that portion—the sample—to gain information about the population. Data are the result of sampling from a population.

Because it takes a lot of time and money to examine an entire population, sampling is a very practical technique. If you wished to compute the overall grade point average at your school, it would make sense to select a sample of students who attend the school. The data collected from the sample would be the students' grade point averages. In presidential elections, opinion poll samples of 1,000–2,000 people are taken. The opinion poll is supposed to represent the views of the people in the entire country. Manufacturers of canned carbonated drinks take samples to determine if a 16-ounce can contains 16 ounces of carbonated drink.

From the sample data, we can calculate a statistic. A statistic is a number that represents a property of the sample. For example, if we consider one math class as a sample of the population of all math classes, then the average number of points earned by students in that one math class at the end of the term is an example of a statistic. Since we do not have the data for all math classes, that statistic is our best estimate of the average for the entire population of math classes. If we happen to have data for all math classes, we can find the population parameter. A parameter is a numerical characteristic of the whole population that can be estimated by a statistic. Since we considered all math classes to be the population, then the average number of points earned per student over all the math classes is an example of a parameter.

One of the main concerns in the field of statistics is how accurately a statistic estimates a parameter. In order to have an accurate sample, it must contain the characteristics of the population in order to be a representative sample . We are interested in both the sample statistic and the population parameter in inferential statistics. In a later chapter, we will use the sample statistic to test the validity of the established population parameter.

A variable , usually notated by capital letters such as X and Y , is a characteristic or measurement that can be determined for each member of a population. Variables may describe values like weight in pounds or favorite subject in school. Numerical variables take on values with equal units such as weight in pounds and time in hours. Categorical variables place the person or thing into a category. If we let X equal the number of points earned by one math student at the end of a term, then X is a numerical variable. If we let Y be a person's party affiliation, then some examples of Y include Republican, Democrat, and Independent. Y is a categorical variable. We could do some math with values of X —calculate the average number of points earned, for example—but it makes no sense to do math with values of Y —calculating an average party affiliation makes no sense.

Data are the actual values of the variable. They may be numbers or they may be words. Datum is a single value.

Two words that come up often in statistics are mean and proportion . If you were to take three exams in your math classes and obtain scores of 86, 75, and 92, you would calculate your mean score by adding the three exam scores and dividing by three. Your mean score would be 84.3 to one decimal place. If, in your math class, there are 40 students and 22 are males and 18 females, then the proportion of men students is 22 40 22 40 and the proportion of women students is 18 40 18 40 . Mean and proportion are discussed in more detail in later chapters.

The words mean and average are often used interchangeably. In this book, we use the term arithmetic mean for mean.

Example 1.1

Determine what the population, sample, parameter, statistic, variable, and data referred to in the following study.

We want to know the mean amount of extracurricular activities in which high school students participate. We randomly surveyed 100 high school students. Three of those students were in 2, 5, and 7 extracurricular activities, respectively.

The population is all high school students.

The sample is the 100 high school students interviewed.

The parameter is the mean amount of extracurricular activities in which all high school students participate.

The statistic is the mean amount of extracurricular activities in which the sample of high school students participate.

The variable could be the amount of extracurricular activities by one high school student. Let X = the amount of extracurricular activities by one high school student.

The data are the number of extracurricular activities in which the high school students participate. Examples of the data are 2, 5, 7.

Find an article online or in a newspaper or magazine that refers to a statistical study or poll. Identify what each of the key terms—population, sample, parameter, statistic, variable, and data—refers to in the study mentioned in the article. Does the article use the key terms correctly?

Example 1.2

Determine what the key terms refer to in the following study.

A study was conducted at a local high school to analyze the average cumulative GPAs of students who graduated last year. Fill in the letter of the phrase that best describes each of the items below.

1. Population ____ 2. Statistic ____ 3. Parameter ____ 4. Sample ____ 5. Variable ____ 6. Data ____

• a) all students who attended the high school last year
• b) the cumulative GPA of one student who graduated from the high school last year
• c) 3.65, 2.80, 1.50, 3.90
• d) a group of students who graduated from the high school last year, randomly selected
• e) the average cumulative GPA of students who graduated from the high school last year
• f) all students who graduated from the high school last year
• g) the average cumulative GPA of students in the study who graduated from the high school last year

1. f ; 2. g ; 3. e ; 4. d ; 5. b ; 6. c

Example 1.3

As part of a study designed to test the safety of automobiles, the National Transportation Safety Board collected and reviewed data about the effects of an automobile crash on test dummies (The Data and Story Library, n.d.). Here is the criterion they used.

Cars with dummies in the front seats were crashed into a wall at a speed of 35 miles per hour. We want to know the proportion of dummies in the driver’s seat that would have had head injuries, if they had been actual drivers. We start with a simple random sample of 75 cars.

The population is all cars containing dummies in the front seat.

The sample is the 75 cars, selected by a simple random sample.

The parameter is the proportion of driver dummies—if they had been real people—who would have suffered head injuries in the population.

The statistic is proportion of driver dummies—if they had been real people—who would have suffered head injuries in the sample.

The variable X = whether driver dummies—if they had been real people—would have suffered head injuries.

The data are either: yes, had head injury, or no, did not.

Example 1.4

An insurance company would like to determine the proportion of all medical doctors who have been involved in one or more malpractice lawsuits. The company selects 500 doctors at random from a professional directory and determines the number in the sample who have been involved in a malpractice lawsuit.

The population is all medical doctors listed in the professional directory.

The parameter is the proportion of medical doctors who have been involved in one or more malpractice suits in the population.

The sample is the 500 doctors selected at random from the professional directory.

The statistic is the proportion of medical doctors who have been involved in one or more malpractice suits in the sample.

The variable X records whether a doctor has or has not been involved in a malpractice suit.

The data are either: yes, was involved in one or more malpractice lawsuits; or no, was not.

Do the following exercise collaboratively with up to four people per group. Find a population, a sample, the parameter, the statistic, a variable, and data for the following study: You want to determine the average—mean—number of glasses of milk college students drink per day. Suppose yesterday, in your English class, you asked five students how many glasses of milk they drank the day before. The answers were 1, 0, 1, 3, and 4 glasses of milk.

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• Authors: Barbara Illowsky, Susan Dean
• Publisher/website: OpenStax
• Book title: Statistics
• Publication date: Mar 27, 2020
• Location: Houston, Texas
• Book URL: https://openstax.org/books/statistics/pages/1-introduction
• Section URL: https://openstax.org/books/statistics/pages/1-1-definitions-of-statistics-probability-and-key-terms

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1.1: Basic Definitions and Concepts

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Learning Objectives

• To learn the basic definitions used in statistics and some of its key concepts.

We begin with a simple example. There are millions of passenger automobiles in the United States. What is their average value? It is obviously impractical to attempt to solve this problem directly by assessing the value of every single car in the country, add up all those values, then divide by the number of values, one for each car. In practice the best we can do would be to estimate the average value. A natural way to do so would be to randomly select some of the cars, say \(200\) of them, ascertain the value of each of those cars, and find the average of those \(200\) values. The set of all those millions of vehicles is called the population of interest, and the number attached to each one, its value, is a measurement . The average value is a parameter : a number that describes a characteristic of the population, in this case monetary worth. The set of \(200\) cars selected from the population is called a sample , and the \(200\) numbers, the monetary values of the cars we selected, are the sample data . The average of the data is called a statistic : a number calculated from the sample data. This example illustrates the meaning of the following definitions.

Definitions: populations and samples

A population is any specific collection of objects of interest. A sample is any subset or subcollection of the population, including the case that the sample consists of the whole population, in which case it is termed a census.

Definitions: measurements and Sample Data

A measurement is a number or attribute computed for each member of a population or of a sample. The measurements of sample elements are collectively called the sample data .

Definition: parameters

A parameter is a number that summarizes some aspect of the population as a whole. A statistic is a number computed from the sample data.

Continuing with our example, if the average value of the cars in our sample was \($8,357\), then it seems reasonable to conclude that the average value of all cars is about \($8,357\). In reasoning this way we have drawn an inference about the population based on information obtained from the sample . In general, statistics is a study of data: describing properties of the data, which is called descriptive statistics , and drawing conclusions about a population of interest from information extracted from a sample, which is called inferential statistics . Computing the single number \($8,357\) to summarize the data was an operation of descriptive statistics; using it to make a statement about the population was an operation of inferential statistics.

Definition: Statistics

Statistics is a collection of methods for collecting, displaying, analyzing, and drawing conclusions from data.

Definition: Descriptive statistics

Descriptive statistics is the branch of statistics that involves organizing, displaying, and describing data.

Definition: Inferential statistics

Inferential statistics is the branch of statistics that involves drawing conclusions about a population based on information contained in a sample taken from that population.

Definition: Qualitative data

Qualitative data are measurements for which there is no natural numerical scale, but which consist of attributes, labels, or other non-numerical characteristics.

Definition: Quantitative data

Quantitative data are numerical measurements that arise from a natural numerical scale.

Qualitative data can generate numerical sample statistics. In the automobile example, for instance, we might be interested in the proportion of all cars that are less than six years old. In our same sample of \(200\) cars we could note for each car whether it is less than six years old or not, which is a qualitative measurement. If \(172\) cars in the sample are less than six years old, which is \(0.86\) or \(86\% \), then we would estimate the parameter of interest, the population proportion, to be about the same as the sample statistic, the sample proportion, that is, about \(0.86\).

The relationship between a population of interest and a sample drawn from that population is perhaps the most important concept in statistics, since everything else rests on it. This relationship is illustrated graphically in Figure \(\PageIndex{1}\). The circles in the large box represent elements of the population. In the figure there was room for only a small number of them but in actual situations, like our automobile example, they could very well number in the millions. The solid black circles represent the elements of the population that are selected at random and that together form the sample. For each element of the sample there is a measurement of interest, denoted by a lower case \(x\) (which we have indexed as \(x_1 , \ldots, x_n\) to tell them apart); these measurements collectively form the sample data set. From the data we may calculate various statistics. To anticipate the notation that will be used later, we might compute the sample mean \(\bar{x}\) and the sample proportion \(\hat{p}\), and take them as approximations to the population mean \(\mu\) (this is the lower case Greek letter mu, the traditional symbol for this parameter) and the population proportion \(p\), respectively. The other symbols in the figure stand for other parameters and statistics that we will encounter.

Key Takeaway

• Statistics is a study of data: describing properties of data (descriptive statistics) and drawing conclusions about a population based on information in a sample (inferential statistics).
• The distinction between a population together with its parameters and a sample together with its statistics is a fundamental concept in inferential statistics.
• Information in a sample is used to make inferences about the population from which the sample was drawn.

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• Tabular Presentation of Data

What is Tabular Presentation of Data in Detail

The presentation of data is essential. A tabular presentation of data helps the viewer to understand and to interpret the information better. Take, for example, your annual report card that is presented in a tabular format. You have your subjects written in one column of the table and your grades on the other. The third column mentions any teachers’ remarks. A single glance at your report card lets you read through the grades and subjects as well as the remarks with ease.

Now think, what would have happened if the same information was presented to you in the form of a paragraph. You would have to go through each line to know the grade that you got and the teachers’ remarks on a particular subject. This would make it tedious and also confusing to understand the report card.

Presentation of Data

Data must be presented properly. If the information is pleasing to the eyes, then it immediately gets attention. Data presentation is about using the same information to exhibit it in an attractive and useful way that can be read and interpreted easily. Data presentation is of three broad kinds. These are:

Textual presentation.

Data tables.

Diagrammatic presentation.

On this presentation of data Class 11 page, you will get to understand the textual and tabular data presentation or the data tables.

Textual Presentation

Data is first obtained in a textual format. It is a vague and raw format of the data. The data is mentioned in the text form, which is usually written in a paragraph. The textual presentation of data is used when the data is not large and can be easily comprehended by the reader just when he reads the paragraph.

This data format is useful when some qualitative statement is to be supplemented with data. The reader does not want to read volumes of data to be represented in the tabular format. Does he want to understand the data in a diagrammatic form? All that the reader wants to know is the data that provides evidence to the statement written. This is enough to let the reader gauge the intensity of the statement.

The textual data is evidence of the qualitative statement, and one needs to go through the complete text before he concludes anything.

For example, the coronavirus death toll in India today is 447. The reader does not need a lot of data here. The entire text of the state-wise breakup is accumulated to arrive at the national death figure. This is enough information for the reader.

Data Tables or Tabular Presentation

Data Tables or Tabular presentation of data is known to be the arrangement of certain values recorded in tables such that they are easy to manage and read. It is mostly done for a reader to gain the idea about the data without making it too complicated. The data presentation can be used for proper matter which is informative and creative at the same time.

What is Data Presentation?

If the reader has to interpret a lot of data, then this has to be organized in an easy to read format. The data should be laid out in rows and columns so that the reader can get what he wants at a single glance. Data tables are easy to construct and also easy to read, which makes them popular.

Components of Data Tables

Below are the key components of the data table.

Table Number - Each table has a table number that makes it easy to locate it. This number serves as a reference and leads one to a particular table.

Title - The table should also have a title that lets the reader understand what information the table provides. The place of study, the period, and the nature of data classification are also mentioned in the title.

Headnotes - The headnotes give further information. It provides the unit of data in brackets which is mentioned at the end of the title. The headnote aids the title to offer more information that the reader would need to interpret the data.

Stubs - These are the titles that tell you what the row represents. In other words, the stubs give information about what data is contained in each row.

Caption - The caption is the column title in the data table. It gives information about what is contained in each column.

Body or Field - The body or the field is the entire content in the table. Each item that is present in the body is the cell.

Footnotes - Footnotes are not commonly used, but these are used to supplement the table title if needed.

Source - If the data used in the table is taken from a secondary source, then that has to be mentioned in the footnote.

Construction of Data Tables

Tabular presentation can be constructed in many ways. Here are some ways that are commonly followed.

The title of the table should be able to reflect on the table content.

If two rows or columns have to be compared, then these should be placed adjacent to each other.

If the rows in the table are lengthy, then the stub can be placed on the right-hand part of the table.

Headings should always be in the singular.

Footnotes are not compulsory and should be provided only if required.

The column size should be symmetrical and uniform.

There should be no abbreviations in the headings and the subheadings.

The units should be specified above the column.

The Advantages of Tabular Presentation

Makes representation of data easy.

Makes it easy to analyze the data.

Makes it easy to compare data.

The data is represented in a readable manner which saves space and the reader’s time.

Classification of Data and Tabular Presentation

Classification of data and Tabular presentation is needed to arrange complex, heterogeneous data into a more simple and sophisticated manner. This is done for the convenience of the audience studying the data so the values are easy to distinguish. There are four ways in which one can classify the data and Tabular presentation. These are as follows.

Qualitative Classification

In qualitative classification, the data is classified based on its qualitative attributes. This is when the data has attributes that cannot be quantified. These could be boys-girls, rural-urban, etc.

Quantitative Classification

In quantitative classification, the data is classified based on the quantitative attributes. These could be marks where the data is categorized into 0-50, 51-100, etc.

Temporal Classification

In this tabular presentation, the data is classified according to the time. Here the data is represented in varied time frames like in the year 2016, 2018, etc.

Spatial Classification

In this method of classification, the data is classified according to location, like India, Pakistan, Russia, etc.

FAQs on Tabular Presentation of Data

1. What do you Mean by the Tabular Presentation of Data?

When data is presented in a tabular form, it makes the information easy to read and to engage. The data is arranged in rows and columns. The tabular method of presenting data is the most widely used. The tabular representation of data coordinates the information for decision making, and any presentation of data in statistics use. Data in the tabular format is divided into 4 kinds. These are the Qualitative (based on traits), Quantitative (based on quantitative features), Temporal (based on time), and spatial (based on location) presentation of data.

2. Explain the Difference Between the Tabular and Textual Presentation of Data ? 

In the tabular representation of data, the data is presented in the form of tables and diagrams. The textual presentation uses words to present the data.Tabular data is self-explanatory as there are segments that depict what the data wants to convey. The textual data need to be explained with words.The key difference thus is that the textual representation of data is subjective. In a tabular format, the data is mentioned in the form of tables. This makes tabular data perfect for the vast amount of data which makes it easy for the reader to read and interpret the information.

3. Where can I get the most appropriate Textual and Tabular Presentation of Data - Advantages, Classification and FAQs?

At Vedantu, the students can find different types of study material which help them ace their exams. Whether it is sample tests, mock tests, important questions, notes you want, Vedantu has it all. All of these are curated by our master teachers who make sure that you score the highest of marks. For finding the Textual and Tabular Presentation of data - Advantages, Classification and FAQs, all students have to do is sign in Vedantu.com using the Vedantu app or website.

4. What is meant by textual and Tabular Presentation? 

Data around us is represented in different ways to us on an everyday basis. Two of these methods are either presenting it via texts which are known as textual presentation and the other one is known as Tabular Presentation by which the data is presented using tables. The tabular presentation is attractive and helps one to visualize the given data, although some may consider textual presentation for a detailed and proper explanation. It depends entirely on the individual how they want their data to be produced, however, most people consider the tabular presentation.

5. Why should I know about textual and Tabular Presentation?

We need data to share information with others, for this, it is important for the students to know how to use the different ways of data presentation. Knowing about Textual and Tabular presentation of data helps an individual to choose how they need their information to be conveyed. Textual data representation is basic and it is important that a student already knows about it completely when they move on to studying the tabular presentation of data. This makes sure that you have your concepts clear and for your progress to attain great heights. 

Refer to Vedantu for free solutions chapter wise and get free access to other online resources to improve your learning in several folds.

Module 5: Choosing and Researching a Topic

Using statistics and data in your speech, learning objectives.

Explain how to use statistics and data in your speech.

Using statistics in public speaking can be a powerful tool. It provides a quantitative, objective, and persuasive platform on which to base an argument, prove a claim, or support an idea. Before a set of statistics can be used, however, it must be made understandable by people who are not familiar with statistics. The key to the persuasive use of statistics is extracting  meaning  and patterns from raw data in a way that is logical and demonstrable to an audience. There are many ways to interpret statistics and data sets, but not all of them are valid.

Guidelines for Helping Your Audience Understand Statistics

• Use reputable sources for the statistics you present in your speech such as government websites, academic institutions and reputable research organizations, and policy/research think tanks.
• Use a large enough sample size in your statistics to make sure that the statistics you are using are accurate (for example, if a survey only asked four people, then it is likely not representative of the population’s viewpoint).
• Use statistics that are easily understood. Many people understand what an average is but not many people will know more complex ideas such as variation and standard deviation.
• When presenting graphs, make sure that the key points are highlighted and the graphs are not misleading as far as the values presented.
• Statistics is a topic that many people prefer to avoid, so when presenting statistical idea or even using numbers in your speech be sure to thoroughly explain what the numbers mean and use visual aids to help you explain.

Communicating Statistics

Graphs, tables, and maps can be used to communicate the numbers, but then the numbers need to be put into context to make the message stick.

Putting Statistics into Context for Our Audiences

We are so used to resorting to statistics that we tend to bombard our audiences with too many mind-numbing numbers. As Chip and Dan Heath state:

Statistics are rarely meaningful in and of themselves. Statistics will, and should, almost always be used to illustrate a relationship. It’s more important for people to remember the relationship than the number. [1]

We need to put statistics into context for our audiences. In their book, the Heaths give several good examples of others who have done this. For example, they introduce us to Geoff Ainscow, one of the leaders of the Beyond War movement in the 1980s.

Ainscow gave talks trying to raise  awareness  of the dangers of nuclear weapons. He wanted to show that the U.S. and the USSR possessed weapons capable of destroying the earth several times over. But simply quoting figures of nuclear weapons stockpiles was not a way to make the message stick. So, after setting the scene, Ainscow would take a BB pellet and drop it into a steel bucket where it would make a loud noise. The pellet represented the bomb that was dropped on Hiroshima. Ainscow would then describe the devastation at Hiroshima. Next, he would take 10 pellets and drop them in the bucket where they made 10 times as much noise. They represented the nuclear firepower on a single nuclear submarine. Finally, he poured 5,000 pellets into the bucket, one for each nuclear warhead in the world. When the noise finally subsided, his audience sat in dead silence.

That is how you put statistics into context.

Using Tables, Graphs and Maps to Communicate Statistical Findings

The story of communicating your statistics does not end with putting them into context. Actually, it would be better to say that it does not begin with putting the numbers into context. In reality, the story you are telling through your  evidence  will probably start with the display of a table, graph, or map.

A simple table, graph, or map can explain a great deal, and so this type of direct evidence should be used where appropriate. However, if a particular part of your analysis represented by a table, graph, or map does not add to or support your argument, it should be left out.

While representing statistical information in tables, graphs, or maps can be highly effective, it is important to ensure that the information is not presented in a manner that can mislead the reader.

A deeper dive: Maps and the electoral college

As this short video from Vox points out, every election cycle we see a map of electoral votes that fails to illustrate—and even conceals—the way electoral votes actually work. In the video (at 1:15), they show a map-based chart by the New York Times that conveys this crucial information much more clearly and accurately than a geographically accurate map of the states. This example should serve as a reminder that maps, like charts, exist to convey information. If the information you’re conveying isn’t captured in a geographic representation—if you’re describing population, for instance, rather than land mass—you might consider a different way to make that information visible to your audience.

You can view the transcript for “The bad map we see every presidential election” here (opens in new window) .

The key to presenting effective tables, graphs, or maps is to ensure they are easy to understand and clearly linked to the message. Ensure that you provide all the necessary information required to understand what the data is showing. The table, graph, or map should be able to stand alone.

Tables, graphs, and maps should  relate directly to the argument,  support statements made in the text,  summarize  relevant  sections of the data analysis, and  be clearly labeled.

Table Checklist

• Use a descriptive title for each table.
• Label every column.
• Provide a source if appropriate.
• Minimize memory load by removing unnecessary data and minimizing decimal places.
• Use clustering and patterns to highlight important relationships.
• Use white space to effect.
• Order data meaningfully (e.g., rank highest to lowest).
• Use a consistent  format  for each table.

Also, do not present too much data in tables. Large expanses of figures can be daunting for an audience, and can obscure your message.

Graph Checklist

• Use a clear, descriptive title.
• Choose the appropriate graph for your message, avoid using 3D graphs as they can obscure information.
• Decide which variable goes on which axis, and what scale is most appropriate.
• If there is more than one data series displayed, always include a legend, preferably within the area of the graph.
• All relevant labels should be included.
• Colors can help differentiate; however, know what is appropriate for the medium you’re using.
• Provide the source of data you’ve used for the graph.
• For readability, it’s generally a good rule of thumb to make the  y -axis three-quarters the size of the  x -axis.

A deeper dive: STorytelling with Data

You can view the transcript for “Telling Stories with Data in 3 Steps (Quick Study)” here (opens in new window) .

• Heath, Chip, and Heath, Dan.  Made to Stick: Why Some Ideas Survive and Others Die . Random House, 2007, 133. ↵
• Using Statistics. Authored by : Boundless. Provided by : Lumen Learning. Located at : https://courses.lumenlearning.com/suny-publicspeakingprinciples/chapter/using-statistics/ . License : CC BY: Attribution
• The bad map we see every presidential election. Provided by : Vox. Located at : https://youtu.be/hlQE4IGFc5A . License : Other . License Terms : Standard YouTube License
• Telling Stories with Data in 3 Steps (Quick Study). Authored by : Harvard Business Review. Located at : https://youtu.be/r5_34YnCmMY . License : Other . License Terms : Standard YouTube License