presentation of data for maths sba

CXC CSEC Mathematics Club

SBA Handbook by Glendon Steele

This Excellent FREE SBA mathematics guide with examples is a Handbook written and produced by Glendon Steele as a guide to students and teachers.  

The Essentials Mathematics Sba Handbook – Glendon Steele

CXC CSEC - Syllabus Mathematics

This is the revised Maths syllabus  Effective from 2018 to present.                         

CSEC – Syllabus Mathematics 2018 to Present – CXC

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CSEC –  Mathematics Past Papers

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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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Helpful Test

Mathematics sba on lunch offered by school canteen.

NOTE: This SBA is a sample/Guide and should NOT be copied and submitted as your own work

How satisfied are students of Helpfultest High School with the lunch services offered by the school canteen?

Introduction

Helpfultest High School has 250 students who primarily use the school canteen for lunch services. The canteen has been serving the staff and students for many years but students have been becoming increasingly agitated with the service that they are receiving. Students complain of different issues with the food and the time it takes to get served. Other students complain about the attitudes of members of the canteen staff while they are being served.

To understand the student’s situations more evidently a team of student researchers decided to do a survey to find out how satisfied the students were with the food and service offered from the canteen.

• How satisfied are students with the food served at the canteen?
• How long on average does it take to be served?
• How satisfied are students with the customer service given?

The data that is collected from the survey will be shared with the canteen staff so decisions can be made on how to improve the services offered by the canteen.

Method of data collection

To gather information about the issues researcher decided to use a survey instrument. A total of 100 students were selected, male and female. There are 5-grade levels and 20 students were taken from each grade level. Each student answered a survey consisting of 11 questions. The results of the survey were then organized and presented.

Survey Questions

• Do you buy or consume any form of cooked lunch from the canteen?
• Approximately how long does it take for you to be served your lunch, from your entry into the canteen until you are served?

How satisfied are you with the length of time it takes to be served?

How satisfied are you with the cost of the lunch?

• How satisfied are you with the amount of food you get when you compare it against the cost?
• How satisfied are you with the presentation of the food?
• What specific aspects of the presentation of the food do you think need improvement? Please state

How satisfied are you with the taste of the food served?

• What specific aspects of the taste of the food do you think need improvement? Please state
• How satisfied are you with the customer service that you receive?
• What specific aspects of the customer service do you think need improvement? Please state 

Analysis of Data

The survey showed that 39% of the people always get their lunch from the canteen while 61% got their lunch from the canteen sometimes. All the persons surveyed were impacted in some way by the canteen. When responding to the time it takes to be served 32% of the persons were served in 10 minutes or less while 68% of the students waited over 10 minutes to be served. The modal interval of time in which students were served was 15 – 20 minutes which had 39%. The mean waiting time was 14 minutes. The data displayed that 72% of the students were either dissatisfied or very dissatisfied with the time they had to wait to be served. Only 28% were satisfied with their waiting time. A total of 97% of the students were satisfied with the price of the lunch. This corresponded with 73% of the students saying they were satisfied with the amount of food they received.

A total of 61% of the students were dissatisfied with the presentation of the food. Their reasons included that the chicken was often over-fried or cut too big to fit in the box. Sometimes too much gravy was put on the food causing lunch boxes to leak and cause the rice to look soggy. A total of 56% of the students were dissatisfied with the taste of the food they got. Some of their reasons included that the food was salty or too fresh, tasted burnt or spoiled.

When students were asked about customer service 45% were dissatisfied and 55% were satisfied. The students mentioned that some staff were kind to them and would accommodate their needs as to what part of the meat they wanted and whether or not they wanted vegetables. Other staff demonstrated a take it or leave it manner.

Students were dissatisfied in three main areas, the length of time it took to be served, the presentation of the food, and the taste of the food. The students were satisfied with the cost of the food, the amount of food they got, and generally with the customer service. 

Discussion of Findings

The researchers found that the average waiting time to be served was 14 minutes. Most students were dissatisfied with that length of time. The researchers also found that the majority of students were satisfied with both the cost of their lunch and the amount of food that they got. A total of 61% were dissatisfied with the presentation of the food served and 56% were dissatisfied with the taste of the food. Only 45% of the students were dissatisfied with the customer service they got. The students were dissatisfied with three areas, time to be served, taste, and presentation while being satisfied with the price, amount of food, and customer service.

The research team can conclude that students are dissatisfied with the length of time they have to wait to be served, the taste of the food, and the presentation of the food. While they are satisfied with the cost, the amount they got and the customer service. It is fair to conclude overall that students generally are not satisfied with their lunches and the services offered by the canteen.

Presentation of Data

The bar chart below shows the frequency with which students use the canteen’s services

The table below shows the length of time it takes for the students to be served

How satisfied are you with the amount of food you get when you compare against the cost

How Satisfied are you with the presentation of the food?

How satisfied are you with the level of customer service that you receive?

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Example of Mathematics SBA ideas and Topic you can choose to create your SBA

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What the New Overtime Rule Means for Workers

One of the basic principles of the American workplace is that a hard day’s work deserves a fair day’s pay. Simply put, every worker’s time has value. A cornerstone of that promise is the  Fair Labor Standards Act ’s (FLSA) requirement that when most workers work more than 40 hours in a week, they get paid more. The  Department of Labor ’s new overtime regulation is restoring and extending this promise for millions more lower-paid salaried workers in the U.S.

Overtime protections have been a critical part of the FLSA since 1938 and were established to protect workers from exploitation and to benefit workers, their families and our communities. Strong overtime protections help build America’s middle class and ensure that workers are not overworked and underpaid.

Some workers are specifically exempt from the FLSA’s minimum wage and overtime protections, including bona fide executive, administrative or professional employees. This exemption, typically referred to as the “EAP” exemption, applies when: 

1. An employee is paid a salary,  

2. The salary is not less than a minimum salary threshold amount, and 

3. The employee primarily performs executive, administrative or professional duties.

While the department increased the minimum salary required for the EAP exemption from overtime pay every 5 to 9 years between 1938 and 1975, long periods between increases to the salary requirement after 1975 have caused an erosion of the real value of the salary threshold, lessening its effectiveness in helping to identify exempt EAP employees.

The department’s new overtime rule was developed based on almost 30 listening sessions across the country and the final rule was issued after reviewing over 33,000 written comments. We heard from a wide variety of members of the public who shared valuable insights to help us develop this Administration’s overtime rule, including from workers who told us: “I would love the opportunity to...be compensated for time worked beyond 40 hours, or alternately be given a raise,” and “I make around $40,000 a year and most week[s] work well over 40 hours (likely in the 45-50 range). This rule change would benefit me greatly and ensure that my time is paid for!” and “Please, I would love to be paid for the extra hours I work!”

The department’s final rule, which will go into effect on July 1, 2024, will increase the standard salary level that helps define and delimit which salaried workers are entitled to overtime pay protections under the FLSA. 

Starting July 1, most salaried workers who earn less than $844 per week will become eligible for overtime pay under the final rule. And on Jan. 1, 2025, most salaried workers who make less than $1,128 per week will become eligible for overtime pay. As these changes occur, job duties will continue to determine overtime exemption status for most salaried employees.

The rule will also increase the total annual compensation requirement for highly compensated employees (who are not entitled to overtime pay under the FLSA if certain requirements are met) from $107,432 per year to $132,964 per year on July 1, 2024, and then set it equal to $151,164 per year on Jan. 1, 2025.

Starting July 1, 2027, these earnings thresholds will be updated every three years so they keep pace with changes in worker salaries, ensuring that employers can adapt more easily because they’ll know when salary updates will happen and how they’ll be calculated.

The final rule will restore and extend the right to overtime pay to many salaried workers, including workers who historically were entitled to overtime pay under the FLSA because of their lower pay or the type of work they performed. 

We urge workers and employers to visit  our website to learn more about the final rule.

Jessica Looman is the administrator for the U.S. Department of Labor’s Wage and Hour Division. Follow the Wage and Hour Division on Twitter at  @WHD_DOL  and  LinkedIn .  Editor's note: This blog was edited to correct a typo (changing "administrator" to "administrative.")

• Wage and Hour Division (WHD)
• Fair Labor Standards Act
• overtime rule

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