graphical representation of data synonyms

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• graphic representation

noun as in alphabet

Strong matches

• fundamentals
• hieroglyphs

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Related words.

Words related to graphic representation are not direct synonyms, but are associated with the word graphic representation . Browse related words to learn more about word associations.

noun as in letters of a writing system

Example Sentences

This astonishingly simple yet devastatingly graphic representation of mass carnage attracts many thousands of visitors every day.

The line is a graphic representation of the vibrations of the membrane and the waves of sound in the air.

While the scheme of graphic representation is entirely different, the facts represented are the same.

Another consequence of the doctrine of valency was that it permitted the graphic representation of the molecule.

Graphic Representation; typical examples of finding a component, a resultant, or an equilibrant.

The graphic representation, therefore, of the motion of each pendulum would be a line as in fig. 4.

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On this page you'll find 14 synonyms, antonyms, and words related to graphic representation, such as: abcs, characters, elements, fundamentals, hieroglyphs, and ideograph.

From Roget's 21st Century Thesaurus, Third Edition Copyright © 2013 by the Philip Lief Group.

Graphical Representation of Data

Graphical representation of data is an attractive method of showcasing numerical data that help in analyzing and representing quantitative data visually. A graph is a kind of a chart where data are plotted as variables across the coordinate. It became easy to analyze the extent of change of one variable based on the change of other variables. Graphical representation of data is done through different mediums such as lines, plots, diagrams, etc. Let us learn more about this interesting concept of graphical representation of data, the different types, and solve a few examples.

Definition of Graphical Representation of Data

A graphical representation is a visual representation of data statistics-based results using graphs, plots, and charts. This kind of representation is more effective in understanding and comparing data than seen in a tabular form. Graphical representation helps to qualify, sort, and present data in a method that is simple to understand for a larger audience. Graphs enable in studying the cause and effect relationship between two variables through both time series and frequency distribution. The data that is obtained from different surveying is infused into a graphical representation by the use of some symbols, such as lines on a line graph, bars on a bar chart, or slices of a pie chart. This visual representation helps in clarity, comparison, and understanding of numerical data.

Representation of Data

The word data is from the Latin word Datum, which means something given. The numerical figures collected through a survey are called data and can be represented in two forms - tabular form and visual form through graphs. Once the data is collected through constant observations, it is arranged, summarized, and classified to finally represented in the form of a graph. There are two kinds of data - quantitative and qualitative. Quantitative data is more structured, continuous, and discrete with statistical data whereas qualitative is unstructured where the data cannot be analyzed.

Principles of Graphical Representation of Data

The principles of graphical representation are algebraic. In a graph, there are two lines known as Axis or Coordinate axis. These are the X-axis and Y-axis. The horizontal axis is the X-axis and the vertical axis is the Y-axis. They are perpendicular to each other and intersect at O or point of Origin. On the right side of the Origin, the Xaxis has a positive value and on the left side, it has a negative value. In the same way, the upper side of the Origin Y-axis has a positive value where the down one is with a negative value. When -axis and y-axis intersect each other at the origin it divides the plane into four parts which are called Quadrant I, Quadrant II, Quadrant III, Quadrant IV. This form of representation is seen in a frequency distribution that is represented in four methods, namely Histogram, Smoothed frequency graph, Pie diagram or Pie chart, Cumulative or ogive frequency graph, and Frequency Polygon.

Advantages and Disadvantages of Graphical Representation of Data

Listed below are some advantages and disadvantages of using a graphical representation of data:

• It improves the way of analyzing and learning as the graphical representation makes the data easy to understand.
• It can be used in almost all fields from mathematics to physics to psychology and so on.
• It is easy to understand for its visual impacts.
• It shows the whole and huge data in an instance.
• It is mainly used in statistics to determine the mean, median, and mode for different data

The main disadvantage of graphical representation of data is that it takes a lot of effort as well as resources to find the most appropriate data and then represent it graphically.

Rules of Graphical Representation of Data

While presenting data graphically, there are certain rules that need to be followed. They are listed below:

• Suitable Title: The title of the graph should be appropriate that indicate the subject of the presentation.
• Measurement Unit: The measurement unit in the graph should be mentioned.
• Proper Scale: A proper scale needs to be chosen to represent the data accurately.
• Index: For better understanding, index the appropriate colors, shades, lines, designs in the graphs.
• Data Sources: Data should be included wherever it is necessary at the bottom of the graph.
• Simple: The construction of a graph should be easily understood.
• Neat: The graph should be visually neat in terms of size and font to read the data accurately.

Uses of Graphical Representation of Data

The main use of a graphical representation of data is understanding and identifying the trends and patterns of the data. It helps in analyzing large quantities, comparing two or more data, making predictions, and building a firm decision. The visual display of data also helps in avoiding confusion and overlapping of any information. Graphs like line graphs and bar graphs, display two or more data clearly for easy comparison. This is important in communicating our findings to others and our understanding and analysis of the data.

Types of Graphical Representation of Data

Data is represented in different types of graphs such as plots, pies, diagrams, etc. They are as follows,

Related Topics

Listed below are a few interesting topics that are related to the graphical representation of data, take a look.

• x and y graph
• Frequency Polygon
• Cumulative Frequency

Examples on Graphical Representation of Data

Example 1 : A pie chart is divided into 3 parts with the angles measuring as 2x, 8x, and 10x respectively. Find the value of x in degrees.

We know, the sum of all angles in a pie chart would give 360º as result. ⇒ 2x + 8x + 10x = 360º ⇒ 20 x = 360º ⇒ x = 360º/20 ⇒ x = 18º Therefore, the value of x is 18º.

Example 2: Ben is trying to read the plot given below. His teacher has given him stem and leaf plot worksheets. Can you help him answer the questions? i) What is the mode of the plot? ii) What is the mean of the plot? iii) Find the range.

Solution: i) Mode is the number that appears often in the data. Leaf 4 occurs twice on the plot against stem 5.

Hence, mode = 54

ii) The sum of all data values is 12 + 14 + 21 + 25 + 28 + 32 + 34 + 36 + 50 + 53 + 54 + 54 + 62 + 65 + 67 + 83 + 88 + 89 + 91 = 958

To find the mean, we have to divide the sum by the total number of values.

Mean = Sum of all data values ÷ 19 = 958 ÷ 19 = 50.42

iii) Range = the highest value - the lowest value = 91 - 12 = 79

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Practice Questions on Graphical Representation of Data

Faqs on graphical representation of data, what is graphical representation.

Graphical representation is a form of visually displaying data through various methods like graphs, diagrams, charts, and plots. It helps in sorting, visualizing, and presenting data in a clear manner through different types of graphs. Statistics mainly use graphical representation to show data.

What are the Different Types of Graphical Representation?

The different types of graphical representation of data are:

• Stem and leaf plot
• Scatter diagrams
• Frequency Distribution

Is the Graphical Representation of Numerical Data?

Yes, these graphical representations are numerical data that has been accumulated through various surveys and observations. The method of presenting these numerical data is called a chart. There are different kinds of charts such as a pie chart, bar graph, line graph, etc, that help in clearly showcasing the data.

What is the Use of Graphical Representation of Data?

Graphical representation of data is useful in clarifying, interpreting, and analyzing data plotting points and drawing line segments , surfaces, and other geometric forms or symbols.

What are the Ways to Represent Data?

Tables, charts, and graphs are all ways of representing data, and they can be used for two broad purposes. The first is to support the collection, organization, and analysis of data as part of the process of a scientific study.

What is the Objective of Graphical Representation of Data?

The main objective of representing data graphically is to display information visually that helps in understanding the information efficiently, clearly, and accurately. This is important to communicate the findings as well as analyze the data.

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2: Graphical Representations of Data

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In this chapter, you will study numerical and graphical ways to describe and display your data. This area of statistics is called "Descriptive Statistics." You will learn how to calculate, and even more importantly, how to interpret these measurements and graphs.

• 2.1: Introduction In this chapter, you will study numerical and graphical ways to describe and display your data. This area of statistics is called "Descriptive Statistics." You will learn how to calculate, and even more importantly, how to interpret these measurements and graphs. In this chapter, we will briefly look at stem-and-leaf plots, line graphs, and bar graphs, as well as frequency polygons, and time series graphs. Our emphasis will be on histograms and box plots.
• 2.2: Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs A stem-and-leaf plot is a way to plot data and look at the distribution, where all data values within a class are visible. The advantage in a stem-and-leaf plot is that all values are listed, unlike a histogram, which gives classes of data values. A line graph is often used to represent a set of data values in which a quantity varies with time. These graphs are useful for finding trends.  A bar graph is a chart that uses either horizontal or vertical bars to show comparisons among categories.
• 2.3: Histograms, Frequency Polygons, and Time Series Graphs A histogram is a graphic version of a frequency distribution. The graph consists of bars of equal width drawn adjacent to each other. The horizontal scale represents classes of quantitative data values and the vertical scale represents frequencies. The heights of the bars correspond to frequency values. Histograms are typically used for large, continuous, quantitative data sets. A frequency polygon can also be used when graphing large data sets with data points that repeat.
• 2.4: Using Excel to Create Graphs Using technology to create graphs will make the graphs faster to create, more precise, and give the ability to use larger amounts of data. This section focuses on using Excel to create graphs.
• 2.5: Graphs that Deceive It's common to see graphs displayed in a misleading manner in social media and other instances. This could be done purposefully to make a point, or it could be accidental. Either way, it's important to recognize these instances to ensure you are not misled.
• 2.E: Graphical Representations of Data (Exercises) These are homework exercises to accompany the Textmap created for "Introductory Statistics" by OpenStax.

Contributors and Attributions

Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/[email protected] .

What Is Data Visualization? Definition, Examples, And Learning Resources

In our increasingly data-driven world, it’s more important than ever to have accessible ways to view and understand data. After all, the demand for data skills in employees is steadily increasing each year. Employees and business owners at every level need to have an understanding of data and of its impact.

That’s where data visualization comes in handy. With the goal of making data more accessible and understandable, data visualization in the form of dashboards is the go-to tool for many businesses to analyze and share information. 

In this article, we'll cover:

• The definition of data visualization
• Advantages and disadvantages of data visualization

Why data visualization is important

Data visualization and big data.

• Data visualization examples
• Tools and software of data visualization
• More about data visualization

What is data visualization?

Data visualization is the graphical representation of information and data. By using v isual elements like charts, graphs, and maps , data visualization tools provide an accessible way to see and understand trends, outliers, and patterns in data. Additionally, it provides an excellent way for employees or business owners to present data to non-technical audiences without confusion.

In the world of Big Data, data visualization tools and technologies are essential to analyze massive amounts of information and make data-driven decisions.

What are the advantages and disadvantages of data visualization?

​​​​Something as simple as presenting data in graphic format may seem to have no downsides. But sometimes data can be misrepresented or misinterpreted when placed in the wrong style of data visualization. When choosing to create a data visualization, it’s best to keep both the advantages and disadvantages in mind. 

Our eyes are drawn to colors and patterns . We can quickly identify red from blue, and squares from circles. Our culture is visual, including everything from art and advertisements to TV and movies. Data visualization is another form of visual art that grabs our interest and keeps our eyes on the message. When we see a chart, we quickly see trends and outliers . If we can see something, we internalize it quickly. It’s storytelling with a purpose. If you’ve ever stared at a massive spreadsheet of data and couldn’t see a trend, you know how much more effective a visualization can be.

Some other advantages of data visualization include:

• Easily sharing information.
• Interactively explore opportunities.
• Visualize patterns and relationships.

Disadvantages

While there are many advantages, some of the disadvantages may seem less obvious. For example, when viewing a visualization with many different datapoints, it’s easy to make an inaccurate assumption. Or sometimes the visualization is just designed wrong so that it’s biased or confusing.

Some other disadvantages include:

• Biased or inaccurate information.
• Correlation doesn’t always mean causation.
• Core messages can get lost in translation.

The importance of data visualization is simple: it helps people see, interact with, and better understand data. Whether simple or complex, the right visualization can bring everyone on the same page, regardless of their level of expertise.

It’s hard to think of a professional industry that doesn’t benefit from making data more understandable . Every STEM field benefits from understanding data—and so do fields in government, finance, marketing, history, consumer goods, service industries, education, sports, and so on. 

While we’ll always wax poetically about data visualization (you’re on the Tableau website, after all) there are practical, real-life applications that are undeniable. And, since visualization is so prolific, it’s also one of the most useful professional skills to develop. The better you can convey your points visually, whether in a dashboard or a slide deck, the better you can leverage that information. The concept of the citizen data scientist is on the rise . Skill sets are changing to accommodate a data-driven world. It is increasingly valuable for professionals to be able to use data to make decisions and use visuals to tell stories of when data informs the who, what, when, where, and how. 

While traditional education typically draws a distinct line between creative storytelling and technical analysis, the modern professional world also values those who can cross between the two: data visualization sits right in the middle of analysis and visual storytelling.

As the “age of Big Data” kicks into high gear , visualization is an increasingly key tool to make sense of the trillions of rows of data generated every day. Data visualization helps to tell stories by curating data into a form easier to understand, highlighting the trends and outliers. A good visualization tells a story, removing the noise from data and highlighting useful information. 

However, it’s not simply as easy as just dressing up a graph to make it look better or slapping on the “info” part of an infographic. Effective data visualization is a delicate balancing act between form and function. The plainest graph could be too boring to catch any notice or it make tell a powerful point; the most stunning visualization could utterly fail at conveying the right message or it could speak volumes. The data and the visuals need to work together, and there’s an art to combining great analysis with great storytelling.

Learn more about big data .

Create beautiful visualizations with your data.

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Examples of data visualization 

Different types of visualizations.

When you think of data visualization, your first thought probably immediately goes to simple bar graphs or pie charts. While these may be an integral part of visualizing data and a common baseline for many data graphics, the right visualization must be paired with the right set of information. Simple graphs are only the tip of the iceberg . There’s a whole selection of visualization methods to present data in effective and interesting ways. 

General Types of Visualizations:

• Chart: Information presented in a tabular, graphical form with data displayed along two axes. Can be in the form of a graph, diagram, or map. Learn more.
• Table: A set of figures displayed in rows and columns. Learn more.
• Graph: A diagram of points, lines, segments, curves, or areas that represents certain variables in comparison to each other, usually along two axes at a right angle. 
• Geospatial: A visualization that shows data in map form using different shapes and colors to show the relationship between pieces of data and specific locations. Learn more.  
• Infographic: A combination of visuals and words that represent data. Usually uses charts or diagrams.
• Dashboards: A collection of visualizations and data displayed in one place to help with analyzing and presenting data. Learn more.

More specific examples

• Area Map: A form of geospatial visualization, area maps are used to show specific values set over a map of a country, state, county, or any other geographic location. Two common types of area maps are choropleths and isopleths. Learn more.
• Bar Chart: Bar charts represent numerical values compared to each other. The length of the bar represents the value of each variable. Learn more. 
• Box-and-whisker Plots: These show a selection of ranges (the box) across a set measure (the bar). Learn more. 
• Bullet Graph: A bar marked against a background to show progress or performance against a goal, denoted by a line on the graph. Learn more.
• Gantt Chart: Typically used in project management, Gantt charts are a bar chart depiction of timelines and tasks. Learn more. 
• Heat Map: A type of geospatial visualization in map form which displays specific data values as different colors (this doesn’t need to be temperatures, but that is a common use). Learn more.
• Highlight Table: A form of table that uses color to categorize similar data, allowing the viewer to read it more easily and intuitively. Learn more. 
• Histogram: A type of bar chart that split a continuous measure into different bins to help analyze the distribution. Learn more. 
• Pie Chart: A circular chart with triangular segments that shows data as a percentage of a whole. Learn more. 
• Treemap: A type of chart that shows different, related values in the form of rectangles nested together. Learn more.

Visualization tools and software

There are dozens of tools for data visualization and data analysis . These range from simple to complex, from intuitive to obtuse. Not every tool is right for every person looking to learn visualization techniques, and not every tool can scale to industry or enterprise purposes. If you’d like to learn more about the options, feel free to read up here or dive into detailed third-party analysis like the Gartner Magic Quadrant.  

Also, remember that good data visualization theory and skills will transcend specific tools and products. When you’re learning this skill, focus on best practices and explore your own personal style when it comes to visualizations and dashboards. Data visualization isn’t going away any time soon, so it’s important to build a foundation of analysis and storytelling and exploration that you can carry with you regardless of the tools or software you end up using.

Learn more about data visualizations 

If you’re feeling inspired or want to learn more, there are tons of resources to tap into. Data visualization and data journalism are full of enthusiastic practitioners eager to share their tips, tricks, theory, and more.

Blogs about data visualization

See our list of great data visualization blogs full of examples, inspiration, and educational resources. The experts who write books and teach classes about the theory behind data visualization also tend to keep blogs where they analyze the latest trends in the field and discuss new vizzes. Many will offer critiques on modern graphics or write tutorials to create effective visualizations. Others will collect many different data visualizations from around the web in order to highlight the most intriguing ones. Blogs are a great way to learn more about specific subsets of data visualization or to look for relatable inspiration from well-done projects.

See our list of the best data visualization blogs.

Books about data visualization

Read our list of great books about data visualization theory and practice. While blogs can keep up with the changing field of data visualization, books focus on where the theory stays constant. Humans have been trying to present data in a visual form throughout our entire existence. One of the earlier books about data visualization, originally published in 1983, set the stage for data visualization to come and still remains relevant to this day. More current books still deal with theory and techniques, offering up timeless examples and practical tips. Some even take completed projects and present the visual graphics in book form as an archival display.

See our list of the best data visualization books.

Courses and Training

There are plenty of great paid and free courses and resources on data visualization out there, including right here on the Tableau website. There are videos, articles, and whitepapers for everyone from beginners to data rockstars. When it comes to third-party courses, however, we won’t provide specific suggestions in this article at this time.

Explore Tableau’s trainings.

Additional Resources

10 interactive map and data visualization examples, tips for creating effective, engaging data visualizations.

Guide On Graphical Representation of Data – Types, Importance, Rules, Principles And Advantages

What are Graphs and Graphical Representation?

Graphs, in the context of data visualization, are visual representations of data using various graphical elements such as charts, graphs, and diagrams. Graphical representation of data , often referred to as graphical presentation or simply graphs which plays a crucial role in conveying information effectively.

Principles of Graphical Representation

Effective graphical representation follows certain fundamental principles that ensure clarity, accuracy, and usability:Clarity : The primary goal of any graph is to convey information clearly and concisely. Graphs should be designed in a way that allows the audience to quickly grasp the key points without confusion.

• Simplicity: Simplicity is key to effective data visualization. Extraneous details and unnecessary complexity should be avoided to prevent confusion and distraction.
• Relevance: Include only relevant information that contributes to the understanding of the data. Irrelevant or redundant elements can clutter the graph.
• Visualization: Select a graph type that is appropriate for the supplied data. Different graph formats, like bar charts, line graphs, and scatter plots, are appropriate for various sorts of data and relationships.

Rules for Graphical Representation of Data

Creating effective graphical representations of data requires adherence to certain rules:

• Select the Right Graph: Choosing the appropriate type of graph is essential. For example, bar charts are suitable for comparing categories, while line charts are better for showing trends over time.
• Label Axes Clearly: Axis labels should be descriptive and include units of measurement where applicable. Clear labeling ensures the audience understands the data’s context.
• Use Appropriate Colors: Colors can enhance understanding but should be used judiciously. Avoid overly complex color schemes and ensure that color choices are accessible to all viewers.
• Avoid Misleading Scaling: Scale axes appropriately to prevent exaggeration or distortion of data. Misleading scaling can lead to incorrect interpretations.
• Include Data Sources: Always provide the source of your data. This enhances transparency and credibility.

Importance of Graphical Representation of Data

Graphical representation of data in statistics is of paramount importance for several reasons:

• Enhances Understanding: Graphs simplify complex data, making it more accessible and understandable to a broad audience, regardless of their statistical expertise.
• Helps Decision-Making: Visual representations of data enable informed decision-making. Decision-makers can easily grasp trends and insights, leading to better choices.
• Engages the Audience: Graphs capture the audience’s attention more effectively than raw data. This engagement is particularly valuable when presenting findings or reports.
• Universal Language: Graphs serve as a universal language that transcends linguistic barriers. They can convey information to a global audience without the need for translation.

Advantages of Graphical Representation

The advantages of graphical representation of data extend to various aspects of communication and analysis:

• Clarity: Data is presented visually, improving clarity and reducing the likelihood of misinterpretation.
• Efficiency: Graphs enable the quick absorption of information. Key insights can be found in seconds, saving time and effort.
• Memorability: Visuals are more memorable than raw data. Audiences are more likely to retain information presented graphically.
• Problem-Solving: Graphs help in identifying and solving problems by revealing trends, correlations, and outliers that may require further investigation.

Use of Graphical Representations

Graphical representations find applications in a multitude of fields:

• Business: In the business world, graphs are used to illustrate financial data, track performance metrics, and present market trends. They are invaluable tools for strategic decision-making.
• Science: Scientists employ graphs to visualize experimental results, depict scientific phenomena, and communicate research findings to both colleagues and the general public.
• Education: Educators utilize graphs to teach students about data analysis, statistics, and scientific concepts. Graphs make learning more engaging and memorable.
• Journalism: Journalists rely on graphs to support their stories with data-driven evidence. Graphs make news articles more informative and impactful.

Types of Graphical Representation

There exists a diverse array of graphical representations, each suited to different data types and purposes. Common types include:

1.Bar Charts:

Used to compare categories or discrete data points, often side by side.

2. Line Charts:

Ideal for showing trends and changes over time, such as stock market performance or temperature fluctuations.

3. Pie Charts:

Display parts of a whole, useful for illustrating proportions or percentages.

4. Scatter Plots:

Reveal relationships between two variables and help identify correlations.

5. Histograms:

Depict the distribution of data, especially in the context of continuous variables.

In conclusion, the graphical representation of data is an indispensable tool for simplifying complex information, aiding in decision-making, and enhancing communication across diverse fields. By following the principles and rules of effective data visualization, individuals and organizations can harness the power of graphs to convey their messages, support their arguments, and drive informed actions.

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FAQs on Graphical Representation of Data

What is the purpose of graphical representation.

Graphical representation serves the purpose of simplifying complex data, making it more accessible and understandable through visual means.

Why are graphs and diagrams important?

Graphs and diagrams are crucial because they provide visual clarity, aiding in the comprehension and retention of information.

How do graphs help learning?

Graphs engage learners by presenting information visually, which enhances understanding and retention, particularly in educational settings.

Who uses graphs?

Professionals in various fields, including scientists, analysts, educators, and business leaders, use graphs to convey data effectively and support decision-making.

Where are graphs used in real life?

Graphs are used in real-life scenarios such as business reports, scientific research, news articles, and educational materials to make data more accessible and meaningful.

Why are graphs important in business?

In business, graphs are vital for analyzing financial data, tracking performance metrics, and making informed decisions, contributing to success.

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Graphical Representation

Graphical representation definition.

Graphical representation refers to the use of charts and graphs to visually display, analyze, clarify, and interpret numerical data, functions, and other qualitative structures. ‍

What is Graphical Representation?

Graphical representation refers to the use of intuitive charts to clearly visualize and simplify data sets. Data is ingested into graphical representation of data software and then represented by a variety of symbols, such as lines on a line chart, bars on a bar chart, or slices on a pie chart, from which users can gain greater insight than by numerical analysis alone. 

Representational graphics can quickly illustrate general behavior and highlight phenomenons, anomalies, and relationships between data points that may otherwise be overlooked, and may contribute to predictions and better, data-driven decisions. The types of representational graphics used will depend on the type of data being explored.

Types of Graphical Representation

Data charts are available in a wide variety of maps, diagrams, and graphs that typically include textual titles and legends to denote the purpose, measurement units, and variables of the chart. Choosing the most appropriate chart depends on a variety of different factors -- the nature of the data, the purpose of the chart, and whether a graphical representation of qualitative data or a graphical representation of quantitative data is being depicted. There are dozens of different formats for graphical representation of data. Some of the most popular charts include:

• Bar Graph -- contains a vertical axis and horizontal axis and displays data as rectangular bars with lengths proportional to the values that they represent; a useful visual aid for marketing purposes
• Choropleth -- thematic map in which an aggregate summary of a geographic characteristic within an area is represented by patterns of shading proportionate to a statistical variable
• Flow Chart -- diagram that depicts a workflow graphical representation with the use of arrows and geometric shapes; a useful visual aid for business and finance purposes
• Heatmap -- a colored, two-dimensional matrix of cells in which each cell represents a grouping of data and each cell’s color indicates its relative value
• Histogram – frequency distribution and graphical representation uses adjacent vertical bars erected over discrete intervals to represent the data frequency within a given interval; a useful visual aid for meteorology and environment purposes
• Line Graph – displays continuous data; ideal for predicting future events over time;  a useful visual aid for marketing purposes
• Pie Chart -- shows percentage values as a slice of pie; a useful visual aid for marketing purposes
• Pointmap -- CAD & GIS contract mapping and drafting solution that visualizes the location of data on a map by plotting geographic latitude and longitude data
• Scatter plot -- a diagram that shows the relationship between two sets of data, where each dot represents individual pieces of data and each axis represents a quantitative measure
• Stacked Bar Graph -- a graph in which each bar is segmented into parts, with the entire bar representing the whole, and each segment representing different categories of that whole; a useful visual aid for political science and sociology purposes
• Timeline Chart -- a long bar labelled with dates paralleling it that display a list of events in chronological order, a useful visual aid for history charting purposes
• Tree Diagram -- a hierarchical genealogical tree that illustrates a family structure; a useful visual aid for history charting purposes
• Venn Diagram -- consists of multiple overlapping usually circles, each representing a set; the default inner join graphical representation

Proprietary and open source software for graphical representation of data is available in a wide variety of programming languages. Software packages often provide spreadsheets equipped with built-in charting functions.

Advantages and Disadvantages of Graphical Representation of Data

Tabular and graphical representation of data are a vital component in analyzing and understanding large quantities of numerical data and the relationship between data points. Data visualization is one of the most fundamental approaches to data analysis, providing an intuitive and universal means to visualize, abstract, and share complex data patterns. The primary advantages of graphical representation of data are:

• Facilitates and improves learning: graphics make data easy to understand and eliminate language and literacy barriers
• Understanding content: visuals are more effective than text in human understanding
• Flexibility of use: graphical representation can be leveraged in nearly every field involving data
• Increases structured thinking: users can make quick, data-driven decisions at a glance with visual aids
• Supports creative, personalized reports for more engaging and stimulating visual  presentations 
• Improves communication: analyzing graphs that highlight relevant themes is significantly faster than reading through a descriptive report line by line
• Shows the whole picture: an instantaneous, full view of all variables, time frames, data behavior and relationships

Disadvantages of graphical representation of data typically concern the cost of human effort and resources, the process of selecting the most appropriate graphical and tabular representation of data, greater design complexity of visualizing data, and the potential for human bias.

Why Graphical Representation of Data is Important

Graphic visual representation of information is a crucial component in understanding and identifying patterns and trends in the ever increasing flow of data. Graphical representation enables the quick analysis of large amounts of data at one time and can aid in making predictions and informed decisions. Data visualizations also make collaboration significantly more efficient by using familiar visual metaphors to illustrate relationships and highlight meaning, eliminating complex, long-winded explanations of an otherwise chaotic-looking array of figures. 

Data only has value once its significance has been revealed and consumed, and its consumption is best facilitated with graphical representation tools that are designed with human cognition and perception in mind. Human visual processing is very efficient at detecting relationships and changes between sizes, shapes, colors, and quantities. Attempting to gain insight from numerical data alone, especially in big data instances in which there may be billions of rows of data, is exceedingly cumbersome and inefficient.

Does HEAVY.AI Offer a Graphical Representation Solution?

HEAVY.AI's visual analytics platform is an interactive data visualization client that works seamlessly with server-side technologies HEAVY.AIDB and Render to enable data science analysts to easily visualize and instantly interact with massive datasets. Analysts can interact with conventional charts and data tables, as well as big data graphical representations such as massive-scale scatterplots and geo charts. Data visualization contributes to a broad range of use cases, including performance analysis in business and guiding research in academia.

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17 Data Visualization Techniques All Professionals Should Know

• 17 Sep 2019

There’s a growing demand for business analytics and data expertise in the workforce. But you don’t need to be a professional analyst to benefit from data-related skills.

Becoming skilled at common data visualization techniques can help you reap the rewards of data-driven decision-making , including increased confidence and potential cost savings. Learning how to effectively visualize data could be the first step toward using data analytics and data science to your advantage to add value to your organization.

Several data visualization techniques can help you become more effective in your role. Here are 17 essential data visualization techniques all professionals should know, as well as tips to help you effectively present your data.

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What Is Data Visualization?

Data visualization is the process of creating graphical representations of information. This process helps the presenter communicate data in a way that’s easy for the viewer to interpret and draw conclusions.

There are many different techniques and tools you can leverage to visualize data, so you want to know which ones to use and when. Here are some of the most important data visualization techniques all professionals should know.

Data Visualization Techniques

The type of data visualization technique you leverage will vary based on the type of data you’re working with, in addition to the story you’re telling with your data .

Here are some important data visualization techniques to know:

• Gantt Chart
• Box and Whisker Plot
• Waterfall Chart
• Scatter Plot
• Pictogram Chart
• Highlight Table
• Bullet Graph
• Choropleth Map
• Network Diagram
• Correlation Matrices

1. Pie Chart

Pie charts are one of the most common and basic data visualization techniques, used across a wide range of applications. Pie charts are ideal for illustrating proportions, or part-to-whole comparisons.

Because pie charts are relatively simple and easy to read, they’re best suited for audiences who might be unfamiliar with the information or are only interested in the key takeaways. For viewers who require a more thorough explanation of the data, pie charts fall short in their ability to display complex information.

2. Bar Chart

The classic bar chart , or bar graph, is another common and easy-to-use method of data visualization. In this type of visualization, one axis of the chart shows the categories being compared, and the other, a measured value. The length of the bar indicates how each group measures according to the value.

One drawback is that labeling and clarity can become problematic when there are too many categories included. Like pie charts, they can also be too simple for more complex data sets.

3. Histogram

Unlike bar charts, histograms illustrate the distribution of data over a continuous interval or defined period. These visualizations are helpful in identifying where values are concentrated, as well as where there are gaps or unusual values.

Histograms are especially useful for showing the frequency of a particular occurrence. For instance, if you’d like to show how many clicks your website received each day over the last week, you can use a histogram. From this visualization, you can quickly determine which days your website saw the greatest and fewest number of clicks.

4. Gantt Chart

Gantt charts are particularly common in project management, as they’re useful in illustrating a project timeline or progression of tasks. In this type of chart, tasks to be performed are listed on the vertical axis and time intervals on the horizontal axis. Horizontal bars in the body of the chart represent the duration of each activity.

Utilizing Gantt charts to display timelines can be incredibly helpful, and enable team members to keep track of every aspect of a project. Even if you’re not a project management professional, familiarizing yourself with Gantt charts can help you stay organized.

5. Heat Map

A heat map is a type of visualization used to show differences in data through variations in color. These charts use color to communicate values in a way that makes it easy for the viewer to quickly identify trends. Having a clear legend is necessary in order for a user to successfully read and interpret a heatmap.

There are many possible applications of heat maps. For example, if you want to analyze which time of day a retail store makes the most sales, you can use a heat map that shows the day of the week on the vertical axis and time of day on the horizontal axis. Then, by shading in the matrix with colors that correspond to the number of sales at each time of day, you can identify trends in the data that allow you to determine the exact times your store experiences the most sales.

6. A Box and Whisker Plot

A box and whisker plot , or box plot, provides a visual summary of data through its quartiles. First, a box is drawn from the first quartile to the third of the data set. A line within the box represents the median. “Whiskers,” or lines, are then drawn extending from the box to the minimum (lower extreme) and maximum (upper extreme). Outliers are represented by individual points that are in-line with the whiskers.

This type of chart is helpful in quickly identifying whether or not the data is symmetrical or skewed, as well as providing a visual summary of the data set that can be easily interpreted.

7. Waterfall Chart

A waterfall chart is a visual representation that illustrates how a value changes as it’s influenced by different factors, such as time. The main goal of this chart is to show the viewer how a value has grown or declined over a defined period. For example, waterfall charts are popular for showing spending or earnings over time.

8. Area Chart

An area chart , or area graph, is a variation on a basic line graph in which the area underneath the line is shaded to represent the total value of each data point. When several data series must be compared on the same graph, stacked area charts are used.

This method of data visualization is useful for showing changes in one or more quantities over time, as well as showing how each quantity combines to make up the whole. Stacked area charts are effective in showing part-to-whole comparisons.

9. Scatter Plot

Another technique commonly used to display data is a scatter plot . A scatter plot displays data for two variables as represented by points plotted against the horizontal and vertical axis. This type of data visualization is useful in illustrating the relationships that exist between variables and can be used to identify trends or correlations in data.

Scatter plots are most effective for fairly large data sets, since it’s often easier to identify trends when there are more data points present. Additionally, the closer the data points are grouped together, the stronger the correlation or trend tends to be.

10. Pictogram Chart

Pictogram charts , or pictograph charts, are particularly useful for presenting simple data in a more visual and engaging way. These charts use icons to visualize data, with each icon representing a different value or category. For example, data about time might be represented by icons of clocks or watches. Each icon can correspond to either a single unit or a set number of units (for example, each icon represents 100 units).

In addition to making the data more engaging, pictogram charts are helpful in situations where language or cultural differences might be a barrier to the audience’s understanding of the data.

11. Timeline

Timelines are the most effective way to visualize a sequence of events in chronological order. They’re typically linear, with key events outlined along the axis. Timelines are used to communicate time-related information and display historical data.

Timelines allow you to highlight the most important events that occurred, or need to occur in the future, and make it easy for the viewer to identify any patterns appearing within the selected time period. While timelines are often relatively simple linear visualizations, they can be made more visually appealing by adding images, colors, fonts, and decorative shapes.

12. Highlight Table

A highlight table is a more engaging alternative to traditional tables. By highlighting cells in the table with color, you can make it easier for viewers to quickly spot trends and patterns in the data. These visualizations are useful for comparing categorical data.

Depending on the data visualization tool you’re using, you may be able to add conditional formatting rules to the table that automatically color cells that meet specified conditions. For instance, when using a highlight table to visualize a company’s sales data, you may color cells red if the sales data is below the goal, or green if sales were above the goal. Unlike a heat map, the colors in a highlight table are discrete and represent a single meaning or value.

13. Bullet Graph

A bullet graph is a variation of a bar graph that can act as an alternative to dashboard gauges to represent performance data. The main use for a bullet graph is to inform the viewer of how a business is performing in comparison to benchmarks that are in place for key business metrics.

In a bullet graph, the darker horizontal bar in the middle of the chart represents the actual value, while the vertical line represents a comparative value, or target. If the horizontal bar passes the vertical line, the target for that metric has been surpassed. Additionally, the segmented colored sections behind the horizontal bar represent range scores, such as “poor,” “fair,” or “good.”

14. Choropleth Maps

A choropleth map uses color, shading, and other patterns to visualize numerical values across geographic regions. These visualizations use a progression of color (or shading) on a spectrum to distinguish high values from low.

Choropleth maps allow viewers to see how a variable changes from one region to the next. A potential downside to this type of visualization is that the exact numerical values aren’t easily accessible because the colors represent a range of values. Some data visualization tools, however, allow you to add interactivity to your map so the exact values are accessible.

15. Word Cloud

A word cloud , or tag cloud, is a visual representation of text data in which the size of the word is proportional to its frequency. The more often a specific word appears in a dataset, the larger it appears in the visualization. In addition to size, words often appear bolder or follow a specific color scheme depending on their frequency.

Word clouds are often used on websites and blogs to identify significant keywords and compare differences in textual data between two sources. They are also useful when analyzing qualitative datasets, such as the specific words consumers used to describe a product.

16. Network Diagram

Network diagrams are a type of data visualization that represent relationships between qualitative data points. These visualizations are composed of nodes and links, also called edges. Nodes are singular data points that are connected to other nodes through edges, which show the relationship between multiple nodes.

There are many use cases for network diagrams, including depicting social networks, highlighting the relationships between employees at an organization, or visualizing product sales across geographic regions.

17. Correlation Matrix

A correlation matrix is a table that shows correlation coefficients between variables. Each cell represents the relationship between two variables, and a color scale is used to communicate whether the variables are correlated and to what extent.

Correlation matrices are useful to summarize and find patterns in large data sets. In business, a correlation matrix might be used to analyze how different data points about a specific product might be related, such as price, advertising spend, launch date, etc.

Other Data Visualization Options

While the examples listed above are some of the most commonly used techniques, there are many other ways you can visualize data to become a more effective communicator. Some other data visualization options include:

• Bubble clouds
• Circle views
• Dendrograms
• Dot distribution maps
• Open-high-low-close charts
• Polar areas
• Radial trees
• Ring Charts
• Sankey diagram
• Span charts
• Streamgraphs
• Wedge stack graphs
• Violin plots

Tips For Creating Effective Visualizations

Creating effective data visualizations requires more than just knowing how to choose the best technique for your needs. There are several considerations you should take into account to maximize your effectiveness when it comes to presenting data.

Related : What to Keep in Mind When Creating Data Visualizations in Excel

One of the most important steps is to evaluate your audience. For example, if you’re presenting financial data to a team that works in an unrelated department, you’ll want to choose a fairly simple illustration. On the other hand, if you’re presenting financial data to a team of finance experts, it’s likely you can safely include more complex information.

Another helpful tip is to avoid unnecessary distractions. Although visual elements like animation can be a great way to add interest, they can also distract from the key points the illustration is trying to convey and hinder the viewer’s ability to quickly understand the information.

Finally, be mindful of the colors you utilize, as well as your overall design. While it’s important that your graphs or charts are visually appealing, there are more practical reasons you might choose one color palette over another. For instance, using low contrast colors can make it difficult for your audience to discern differences between data points. Using colors that are too bold, however, can make the illustration overwhelming or distracting for the viewer.

Related : Bad Data Visualization: 5 Examples of Misleading Data

Visuals to Interpret and Share Information

No matter your role or title within an organization, data visualization is a skill that’s important for all professionals. Being able to effectively present complex data through easy-to-understand visual representations is invaluable when it comes to communicating information with members both inside and outside your business.

There’s no shortage in how data visualization can be applied in the real world. Data is playing an increasingly important role in the marketplace today, and data literacy is the first step in understanding how analytics can be used in business.

Are you interested in improving your analytical skills? Learn more about Business Analytics , our eight-week online course that can help you use data to generate insights and tackle business decisions.

This post was updated on January 20, 2022. It was originally published on September 17, 2019.

About the Author

• School Guide
• Class 9 Syllabus
• Maths Notes Class 9
• Science Notes Class 9
• History Notes Class 9
• Geography Notes Class 9
• Political Science Notes Class 9
• NCERT Soln. Class 9 Maths
• RD Sharma Soln. Class 9
• Math Formulas Class 9
• CBSE Class 9 Maths Revision Notes

Chapter 1: Number System

• Number System in Maths
• Natural Numbers | Definition, Examples, Properties
• Whole Numbers | Definition, Properties and Examples
• Rational Number: Definition, Examples, Worksheet
• Irrational Numbers- Definition, Identification, Examples, Symbol, Properties
• Real Numbers
• Decimal Expansion of Real Numbers
• Decimal Expansions of Rational Numbers
• Representation of Rational Numbers on the Number Line | Class 8 Maths
• Represent √3 on the number line
• Operations on Real Numbers
• Rationalization of Denominators
• Laws of Exponents for Real Numbers

Chapter 2: Polynomials

• Polynomials in One Variable - Polynomials | Class 9 Maths
• Polynomial Formula
• Types of Polynomials
• Zeros of Polynomial
• Factorization of Polynomial
• Remainder Theorem
• Factor Theorem
• Algebraic Identities

Chapter 3: Coordinate Geometry

• Coordinate Geometry
• Cartesian Coordinate System in Maths
• Cartesian Plane

Chapter 4: Linear equations in two variables

• Linear Equations in One Variable
• Linear Equation in Two Variables
• Graph of Linear Equations in Two Variables
• Graphical Methods of Solving Pair of Linear Equations in Two Variables
• Equations of Lines Parallel to the x-axis and y-axis

Chapter 5: Introduction to Euclid's Geometry

• Euclidean Geometry
• Equivalent Version of Euclid’s Fifth Postulate

Chapter 6: Lines and Angles

• Lines and Angles
• Types of Angles
• Pairs of Angles - Lines & Angles
• Transversal Lines
• Angle Sum Property of a Triangle

Chapter 7: Triangles

• Triangles in Geometry
• Congruence of Triangles |SSS, SAS, ASA, and RHS Rules
• Theorem - Angle opposite to equal sides of an isosceles triangle are equal | Class 9 Maths
• Triangle Inequality Theorem, Proof & Applications

Chapter 8: Quadrilateral

• Angle Sum Property of a Quadrilateral
• Quadrilateral - Definition, Properties, Types, Formulas, Examples
• Introduction to Parallelogram: Properties, Types, and Theorem
• Rhombus: Definition, Properties, Formula, Examples
• Kite - Quadrilaterals
• Properties of Parallelograms
• Mid Point Theorem

Chapter 9: Areas of Parallelograms and Triangles

• Area of Triangle | Formula and Examples
• Area of Parallelogram
• Figures on the Same Base and between the Same Parallels

Chapter 10: Circles

• Circles in Maths
• Radius of Circle
• Tangent to a Circle
• What is the longest chord of a Circle?
• Circumference of Circle - Definition, Perimeter Formula, and Examples
• Angle subtended by an arc at the centre of a circle
• What is Cyclic Quadrilateral
• Theorem - The sum of opposite angles of a cyclic quadrilateral is 180° | Class 9 Maths

Chapter 11: Construction

• Basic Constructions - Angle Bisector, Perpendicular Bisector, Angle of 60°
• Construction of Triangles

Chapter 12: Heron's Formula

• Area of Equilateral Triangle
• Area of Isosceles Triangle
• Heron's Formula
• Applications of Heron's Formula
• Area of Quadrilateral
• Area of Polygons

Chapter 13: Surface Areas and Volumes

• Surface Area of Cuboid
• Volume of Cuboid | Formula and Examples
• Surface Area of Cube
• Volume of a Cube
• Surface Area of Cylinder (CSA and TSA) |Formula, Derivation, Examples
• Volume of Cylinder
• Surface Area of Cone
• Volume of Cone | Formula, Derivation and Examples
• Surface Area of Sphere | CSA, TSA, Formula and Derivation
• Volume of a Sphere
• Surface Area of a Hemisphere
• Volume of Hemisphere

Chapter 14: Statistics

• Collection and Presentation of Data

Graphical Representation of Data

• Bar graphs and Histograms
• Central Tendency
• Mean, Median and Mode

Chapter 15: Probability

• Experimental Probability
• Empirical Probability
• CBSE Class 9 Maths Formulas
• NCERT Solutions for Class 9 Maths
• RD Sharma Class 9 Solutions

In today’s world of the internet and connectivity, there is a lot of data available and some or the other method is needed for looking at large data, the patterns, and trends in it. There is an entire branch in mathematics dedicated to dealing with collecting, analyzing, interpreting, and presenting the numerical data in visual form in such a way that it becomes easy to understand and the data becomes easy to compare as well, the branch is known as Statistics . The branch is widely spread and has a plethora of real-life applications such as Business Analytics, demography, astrostatistics, and so on. There are two ways of representing data, 

• Pictorial Representation through graphs.

They say, “A picture is worth the thousand words”.  It’s always better to represent data in graphical format. Even in Practical Evidence and Surveys, scientists have found that the restoration and understanding of any information is better when it is available in form of visuals as Human beings process data better in visual form than any other form. Does it increase the ability 2 times or 3 times? The answer is it increases the Power of understanding 60,000 times for a normal Human being, the fact is amusing and true at the same time. Let’s look at some of them in detail. 

Types of Graphical Representations

Comparison between different items is best shown with graphs, it becomes easier to compare the crux out of the data pertaining to different items. Let’s look at all the different types of graphical representations briefly: 

Line Graphs

A line graph is used to show how the value of particular variable changes with time. We plot this graph by connecting the points at different values of the variable. It can be useful for analyzing the trends in the data predicting further trends. 

A bar graph is a type of graphical representation of the data in which bars of uniform width are drawn with equal spacing between them on one axis (x-axis usually), depicting the variable. The values of the variables are represented by the height of the bars. 

Histograms 

This is similar to bar graphs, but it is based frequency of numerical values rather than their actual values. The data is organized into intervals and the bars represent the frequency of the values in that range. That is, it counts how many values of the data lie in a particular range. 

Line Plot 

It is a plot that displays data as points and checkmarks above a number line, showing the frequency of the point. 

Stem and Leaf Plot 

This is a type of plot in which each value is split into a “leaf”(in most cases, it is the last digit) and “stem”(the other remaining digits). For example: the number 42 is split into leaf (2) and stem (4).  

Box and Whisker Plot 

These plots divide the data into four parts to show their summary. They are more concerned about the spread, average, and median of the data. 

It is a type of graph which represents the data in form of a circular graph. The circle is divided such that each portion represents a proportion of the whole. 

Graphical Representations used in Maths

Graphs in maths are used to study the relationships between two or more variables that are changing. Statistical data can be summarized in a better way using graphs. There are basically two lines of thoughts of making graphs in maths: 

• Value-Based or Time Series Graphs

Frequency Based

Value-based or time series graphs .

These graphs allow us to study the change of a variable with respect to another variable within a given interval of time. The variables can be anything. Time Series graphs study the change of variable with time. They study the trends, periodic behavior, and patterns in the series. We are more concerned with the values of the variables here rather than the frequency of those values. 

Example: Line Graph

These kinds of graphs are more concerned with the distribution of data. How many values lie between a particular range of the variables, and which range has the maximum frequency of the values. They are used to judge a spread and average and sometimes median of a variable under study. 

Example: Frequency Polygon, Histograms.

Principles of Graphical Representations

All types of graphical representations require some rule/principles which are to be followed. These are some algebraic principles. When we plot a graph, there is an origin, and we have our two axes. These two axes divide the plane into four parts called quadrants. The horizontal one is usually called the x-axis and the other one is called the y-axis. The origin is the point where these two axes intersect. The thing we need to keep in mind about the values of the variable on the x-axis is that positive values need to be on the right side of the origin and negative values should be on the left side of the origin. Similarly, for the variable on the y-axis, we need to make sure that the positive values of this variable should be above the x-axis and negative values of this variable must be below the y-axis. 

Advantages and Disadvantages of using Graphical System

Advantages: 

• It gives us a summary of the data which is easier to look at and analyze.
• It saves time.
• We can compare and study more than one variable at a time.

Disadvantage: 

It usually takes only one aspect of the data and ignores the other. For example, A bar graph does not represent the mean, median, and other statistics of the data. 

General Rules for Graphical Representation of Data

We should keep in mind some things while plotting and designing these graphs. The goal should be a better and clear picture of the data. Following things should be kept in mind while plotting the above graphs: 

• Whenever possible, the data source must be mentioned for the viewer.
• Always choose the proper colors and font sizes. They should be chosen to keep in mind that the graphs should look neat.
• The measurement Unit should be mentioned in the top right corner of the graph.
• The proper scale should be chosen while making the graph, it should be chosen such that the graph looks accurate.
• Last but not the least, a suitable title should be chosen.

Frequency Polygon

A frequency polygon is a graph that is constructed by joining the midpoint of the intervals. The height of the interval or the bin represents the frequency of the values that lie in that interval. 

Sample Problems

Question 1: What are different types of frequency-based plots? 

Answer: 

Types of frequency based plots:  Histogram Frequency Polygon Box Plots

Question 2: A company with an advertising budget of Rs 10,00,00,000 has planned the following expenditure in the different advertising channels such as TV Advertisement, Radio, Facebook, Instagram, and Printed media. The table represents the money spent on different channels. 

Draw a bar graph for the following data. 

Solution: 

Steps:  Put each of the channels on the x-axis The height of the bars is decided by the value of each channel.

Question 3: Draw a line plot for the following data 

Steps:  Put each of the x-axis row value on the x-axis joint the value corresponding to the each value of the x-axis.

Question 4: Make a frequency plot of the following data: 

Steps:  Draw the class intervals on the x-axis and frequencies on the y-axis. Calculate the mid point of each class interval. Class Interval Mid Point Frequency 0-3 1.5 3 3-6 4.5 4 6-9 7.5 2 9-12 10.5 6 Now join the mid points of the intervals and their corresponding frequencies on the graph.  This graph shows both the histogram and frequency polygon for the given distribution.

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Graphical Representation

Graphical Representation is a way of analysing numerical data. It exhibits the relation between data, ideas, information and concepts in a diagram. It is easy to understand and it is one of the most important learning strategies. It always depends on the type of information in a particular domain. There are different types of graphical representation. Some of them are as follows:

• Line Graphs – Line graph or the linear graph is used to display the continuous data and it is useful for predicting future events over time.
• Bar Graphs – Bar Graph is used to display the category of data and it compares the data using solid bars to represent the quantities.
• Histograms – The graph that uses bars to represent the frequency of numerical data that are organised into intervals. Since all the intervals are equal and continuous, all the bars have the same width.
• Line Plot – It shows the frequency of data on a given number line. ‘ x ‘ is placed above a number line each time when that data occurs again.
• Frequency Table – The table shows the number of pieces of data that falls within the given interval.
• Circle Graph – Also known as the pie chart that shows the relationships of the parts of the whole. The circle is considered with 100% and the categories occupied is represented with that specific percentage like 15%, 56%, etc.
• Stem and Leaf Plot – In the stem and leaf plot, the data are organised from least value to the greatest value. The digits of the least place values from the leaves and the next place value digit forms the stems.
• Box and Whisker Plot – The plot diagram summarises the data by dividing into four parts. Box and whisker show the range (spread) and the middle ( median) of the data.

General Rules for Graphical Representation of Data

There are certain rules to effectively present the information in the graphical representation. They are:

• Suitable Title: Make sure that the appropriate title is given to the graph which indicates the subject of the presentation.
• Measurement Unit: Mention the measurement unit in the graph.
• Proper Scale: To represent the data in an accurate manner, choose a proper scale.
• Index: Index the appropriate colours, shades, lines, design in the graphs for better understanding.
• Data Sources: Include the source of information wherever it is necessary at the bottom of the graph.
• Keep it Simple: Construct a graph in an easy way that everyone can understand.
• Neat: Choose the correct size, fonts, colours etc in such a way that the graph should be a visual aid for the presentation of information.

Graphical Representation in Maths

In Mathematics, a graph is defined as a chart with statistical data, which are represented in the form of curves or lines drawn across the coordinate point plotted on its surface. It helps to study the relationship between two variables where it helps to measure the change in the variable amount with respect to another variable within a given interval of time. It helps to study the series distribution and frequency distribution for a given problem.  There are two types of graphs to visually depict the information. They are:

• Time Series Graphs – Example: Line Graph
• Frequency Distribution Graphs – Example: Frequency Polygon Graph

Principles of Graphical Representation

Algebraic principles are applied to all types of graphical representation of data. In graphs, it is represented using two lines called coordinate axes. The horizontal axis is denoted as the x-axis and the vertical axis is denoted as the y-axis. The point at which two lines intersect is called an origin ‘O’. Consider x-axis, the distance from the origin to the right side will take a positive value and the distance from the origin to the left side will take a negative value. Similarly, for the y-axis, the points above the origin will take a positive value, and the points below the origin will a negative value.

Generally, the frequency distribution is represented in four methods, namely

• Smoothed frequency graph
• Pie diagram
• Cumulative or ogive frequency graph
• Frequency Polygon

Merits of Using Graphs

Some of the merits of using graphs are as follows:

• The graph is easily understood by everyone without any prior knowledge.
• It saves time
• It allows us to relate and compare the data for different time periods
• It is used in statistics to determine the mean, median and mode for different data, as well as in the interpolation and the extrapolation of data.

Example for Frequency polygonGraph

Here are the steps to follow to find the frequency distribution of a frequency polygon and it is represented in a graphical way.

• Obtain the frequency distribution and find the midpoints of each class interval.
• Represent the midpoints along x-axis and frequencies along the y-axis.
• Plot the points corresponding to the frequency at each midpoint.
• Join these points, using lines in order.
• To complete the polygon, join the point at each end immediately to the lower or higher class marks on the x-axis.

Draw the frequency polygon for the following data

Mark the class interval along x-axis and frequencies along the y-axis.

Let assume that class interval 0-10 with frequency zero and 90-100 with frequency zero.

Now calculate the midpoint of the class interval.

Using the midpoint and the frequency value from the above table, plot the points A (5, 0), B (15, 4), C (25, 6), D (35, 8), E (45, 10), F (55, 12), G (65, 14), H (75, 7), I (85, 5) and J (95, 0).

To obtain the frequency polygon ABCDEFGHIJ, draw the line segments AB, BC, CD, DE, EF, FG, GH, HI, IJ, and connect all the points.

Frequently Asked Questions

What are the different types of graphical representation.

Some of the various types of graphical representation include:

• Line Graphs
• Frequency Table
• Circle Graph, etc.

Read More:  Types of Graphs

What are the Advantages of Graphical Method?

Some of the advantages of graphical representation are:

• It makes data more easily understandable.
• It saves time.
• It makes the comparison of data more efficient.

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Very useful for understand the basic concepts in simple and easy way. Its very useful to all students whether they are school students or college sudents

Thanks very much for the information

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Unit 5: Represent and interpret data

Picture graphs.

• Creating picture and bar graphs (Opens a modal)
• Creating picture graphs (Opens a modal)
• Solving problems with picture graphs (Opens a modal)
• Reading picture graphs (Opens a modal)
• Interpreting picture graphs: paint (Opens a modal)
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• Reading picture graphs: multi-step (Opens a modal)
• Create picture graphs (picture more than 1) Get 5 of 7 questions to level up!
• Read picture graphs Get 5 of 7 questions to level up!
• Read picture graphs (multi-step problems) Get 3 of 4 questions to level up!
• Creating bar graphs (Opens a modal)
• Reading bar graphs: Harry Potter (Opens a modal)
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Line plots with fractions

• Measuring lengths to nearest 1/4 unit (Opens a modal)
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• Line plots review (Opens a modal)
• Measure lengths to nearest 1/4 unit Get 3 of 4 questions to level up!
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Computer Science > Computation and Language

Title: unveiling llms: the evolution of latent representations in a temporal knowledge graph.

Abstract: Large Language Models (LLMs) demonstrate an impressive capacity to recall a vast range of common factual knowledge information. However, unravelling the underlying reasoning of LLMs and explaining their internal mechanisms of exploiting this factual knowledge remain active areas of investigation. Our work analyzes the factual knowledge encoded in the latent representation of LLMs when prompted to assess the truthfulness of factual claims. We propose an end-to-end framework that jointly decodes the factual knowledge embedded in the latent space of LLMs from a vector space to a set of ground predicates and represents its evolution across the layers using a temporal knowledge graph. Our framework relies on the technique of activation patching which intervenes in the inference computation of a model by dynamically altering its latent representations. Consequently, we neither rely on external models nor training processes. We showcase our framework with local and global interpretability analyses using two claim verification datasets: FEVER and CLIMATE-FEVER. The local interpretability analysis exposes different latent errors from representation to multi-hop reasoning errors. On the other hand, the global analysis uncovered patterns in the underlying evolution of the model's factual knowledge (e.g., store-and-seek factual information). By enabling graph-based analyses of the latent representations, this work represents a step towards the mechanistic interpretability of LLMs.

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