BrightChamps Logo
Login
Creative Math Ideas Image
Live Math Learners Count Icon2246 Learners

Last updated on July 4th, 2025

Math Whiteboard Illustration

Frequency Distribution Table

Professor Greenline Explaining Math Concepts

A frequency distribution table is a chart that presents the frequency of each category or data in an organized way. It represents how often each value occurs and helps identify patterns within a dataset. When collecting data, we need to organize the data into a frequency distribution table. This table summarizes the data by grouping it into different categories or variables, and their frequencies. In this topic, we will learn the essentials of the frequency distribution table and its properties.

Frequency Distribution Table for Thai Students
Professor Greenline from BrightChamps

What is a Frequency Distribution?

In a dataset, how often something occurs is expressed by its frequency. In statistics, frequency distribution is a tool that is used for data organization and to make meaningful decisions. How often a value appears in a dataset can be understood by a frequency distribution. It shows where the most values are concentrated and where the least values are presented. Tabularly or graphically, we can represent the frequency distribution.

Professor Greenline from BrightChamps

Frequency Distribution Graphs

To visually represent a frequency distribution table, we use a frequency distribution graph. Graphical elements, such as bars, lines, and curves are used to express how frequently various values occur. These graphs help us to simplify complex data, figure out new trends, and make informed decisions. The various methods for representing the frequency distribution are:

 

Histogram 

A histogram is used for representing numerical data, and it is similar to a bar graph. The y-axis of the histogram indicates frequencies, and the x-axis represents interval classes. Remember, there is no gap between the bars of a histogram. For example, here is a frequency table explaining the number of survey respondents in each age group.

 

Age (years) Frequency
10 - 20 10
20 - 30  15
30 - 40 5
40 - 50 5
50 - 60 3

 

The histogram showing the ages of survey respondents is:

NA

 

Bar graph

Bar graphs use rectangular bars to represent the data on the x-axis and y-axis. The height and length of the bars show the frequency of categories or values. The bar graph is commonly used to express the frequency of ungrouped data in a flexible sequence. Remember to always leave gaps between the bars to separate the categories clearly. For e.g., the distribution table representing a dataset of kids and their favorite ice cream flavors will look like this:

 

Ice cream flavor Number of kids (frequency)
Vanilla 6
Chocolate  7
Strawberry 3
Mango 4
Butterscotch   8

 

The following is a bar graph representing the frequency of kids and their favorite ice cream flavors.

NA

 

Frequency polygon 

In a frequency polygon, the data is visually represented by plotting dots at the midpoints of each class interval and joining them with straight lines to form a polygon. For example, here is a dataset that shows the number of young people enjoying different genres of movies.

 

Movies Number of Young People (frequency)
Action 72
Science fiction 55
Comedy  40
Horror  42
Romance  38

 

Here is the frequency polygon, representing the frequency of youth and their favorite movie genres. 

NA

 

Pie chart

The pie chart represents data in a circular format. Each category is represented as a slice of an entire circle, and the size of each slice shows its proportion of the total dataset. For example, the frequency distribution table of kids who prefer different fruits is given below:

 

Fruit  Number of kids (frequency)
Apple 8
Orange 5
Pineapple 7
Strawberry 4
Mango 6

 

Here, the pie chart of the given frequency distribution table is given below. 

Here, when we convert a number into a percentage, use the formula:
Percentage = Frequency of a category / Total frequency × 100 
So, total frequency = 8 + 5  + 7 + 4 + 6 = 30

 

Frequency of Apple = 8 / 30 × 100 = 26. 7%

Frequency of Orange = 5/ 30 × 100 = 16.7%

Frequency of Pineapple = 7/ 30 × 100 = 23.3%

Frequency of Strawberry = 4 / 30 × 100 = 13.3%

Frequency of Mango =  6 / 30 × 100 = 20

Professor Greenline from BrightChamps

What are the Types of Frequency Distribution?

Depending on the nature of the collected data, frequency distribution is classified into different types. The collected data is organized in a meaningful way to clearly understand the nature, pattern, and trends and to make better decisions. The four types of frequency distribution are:

Professor Greenline from BrightChamps

Grouped frequency distribution

The observations or data in a grouped frequency distribution are divided into different intervals. Then, the frequencies of each class interval are counted. When we have a very large set of data, this type of frequency distribution is useful to make data much easier to understand.

 

For example, the data given in a grouped frequency distribution is categorized into different groups of equal sizes. Then, the number of times each class interval or category appears is marked against each interval. The frequency distribution table for grouped data is given below:

 

Weight of students Number of students (frequency
25 - 30 3
31 - 35 6
36 - 40 5
41 - 45 2

 

Professor Greenline from BrightChamps

Ungrouped frequency distribution

In an ungrouped frequency distribution, the distinct observations or data are collected and counted separately. When we have a small dataset, the ungrouped frequency distribution is useful. For instance, if we have to count the marks of 15 students in a class, we can apply this type of frequency distribution. The frequency distribution table of an ungrouped dataset is:

 

Marks scored Number of students (frequency)
5 1
11 3
16 1
22 2
27 4
35 2
40 2

 

Professor Greenline from BrightChamps

Relative frequency distribution

The percentage or proportion of observations in each class is represented by relative frequency distribution. We use this type of distribution to compare several data sets or to understand the distribution of data within a single set by expressing frequencies as percentages. The formula for relative frequency is:
Relative frequency = Frequency of event / total number of events
For example, the relative frequency distribution table for the following data is:

 

Marks scored Number of kids (frequency)
0 - 10 8
11 - 20 5
21 - 30 7
31 - 40 4
41 - 50  6

 

 The relative frequency distribution table:

 

Marks scored Number of kids (frequency) Relative frequency
0 - 10 8 8 / 30 = 0.26
11 - 20 5 5 / 30 = 0.16
21 - 30 7 7 / 30 = 0.23
31 - 40 4 4 / 30 = 0.13
41 - 50  6 6 / 30 = 0.20

 

Professor Greenline from BrightChamps

Cumulative frequency distribution

Cumulative frequency is the running total of all frequencies up to a specific value or interval. The two types of cumulative frequency distributions are:

 

  • Less than cumulative frequency
    It refers to the sum of all frequencies up to and including a given interval. 

 

  • More than cumulative frequency
    It refers to the sum of all the frequencies from a given interval onward. 
    For example, we collected the values of marks scored by Miya on her last 18 exams.

 

45 34 75
26 9 50
97 8 15
57 88 86
33 47 63
64 70 74

 

Here, we have a lot of distinct values. So, we will categorize these values in a grouped distribution frequency table.

 

Marks  Frequency
0 - 10  2
10 - 20  1
20 - 30 1
30 - 40 2
40 - 50  3
50 - 60 1
60 - 70 3
70 - 80 2
80 - 90 2
90 - 100  1

 

Next, we can convert this frequency distribution table into a cumulative frequency distribution table.

 

Marks scored by Miya Cumulative frequency
Less than 10  2
Less than 20 2 + 1 = 3 
Less than 30 4
Less than 40 6
Less than 50 9
Less than 60  10
Less than 70 13
Less than 80 15
Less than 90 17
Less than 100 18

 

Next, the cumulative frequency distribution of the second type which is more than cumulative frequency.

 

Marks scored by Miya Cumulative frequency
More than 10  18
More than 20 18 - 2 = 16
More than 30  15
More than 40 14
More than 50 12
More than 60 9
More than 70 8
More than 80 5
More than 90 3
More than 100 1

 

Professor Greenline from BrightChamps

How to Make a Frequency Distribution Table?

While making a frequency distribution table, we have to adhere to several steps. They are as follows:

 

Step 1: Design a table with two columns. One for frequency and the other for the data we need to organize. 

 

Step 2: Decide whether we need a grouped frequency distribution table or an ungrouped frequency distribution table by analyzing the items in the given dataset. When we have a very large set of data, then better we go with a grouped frequency distribution table. 

 

Step 3: In the first column, categorize the data set values. 

 

Step 4: Identify the frequency of each category by counting them and allocate it to the second column. 

 

Step 5: Finally, write the total frequency in the last row of the frequency distribution table. 

 

By following these steps, we can create an organized and well-structured frequency distribution table for the given dataset.

Professor Greenline from BrightChamps

Real-Life Applications of Frequency Distribution Table

Frequency distribution is a tool used in statistics to organize data and make insightful conclusions. A frequency distribution table is a chart that presents the frequency of each category or data in an organized way. It represents how often each value occurs in a given dataset. The real-life applications of the frequency distribution table are countless. They are given below.

 

  • To determine the number of goods and services sold by a shop or company, the businesses use the frequency distribution table. It helps them track their sales and to analyze the feedback of their customers. 

 

  • In the field of education, teachers and educational institutions can categorize the marks of their students and analyze the performance of the students. They can keep records of the marks scored by the students in each examination. 

 

  • To track the frequency of a disease based on age, blood groups, or patient locations, hospitals, and healthcare professionals use the frequency distribution table. 

 

  • To evaluate the income levels in a population, categorize expenditure levels, and analyze stock prices within a certain range, political critics, government officials, and economists can use the frequency distribution table for their research and studies. 

 

  • In the fields of sports, public transportation, and social media, the frequency distribution table plays a vital role in organizing data into several categories.
Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them on Frequency Distribution Table

Frequency distribution tables are crucial for comparing multiple sets of data easily. It represents the data in a structured manner, and it allows us to understand the different trends and patterns from the dataset. However, some common mistakes can lead us to incorrect calculations and conclusions. Here are some of the common errors and their solutions that will help to obtain better results.

Mistake 1

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Applying unequal class intervals

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Students should use consistent class widths or intervals in the distribution tables. Otherwise, it will lead to incorrect results. For example, sometimes, kids make a frequency distribution table with different class intervals, such as 0 - 5, 5 - 15, 15 - 25, and so on. In order to avoid this mistake, use a consistent class width like 0 - 10, 11 - 20, 21 - 30, and so on.

Mistake 2

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Forget to include all data values

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Cross-check the results before finalizing them. From the given dataset, all the raw data will be included in the frequency distribution table. If we skipped any data point, then the analysis will be wrong. It will affect the total frequencies and does not match the final results.

Mistake 3

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Considering too many or too few classes

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Depending on the dataset, we have to use the proper class width for the frequency distribution table. Using too many classes makes the final result difficult to interpret and find the trends and patterns. Likewise, using too few classes will lead to the loss of important data and the table loses its balanced view of the dataset.

Mistake 4

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Improperly labeling the table

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

When we create a frequency distribution table, remember to include column names in the proper places. In a frequency distribution table, there are two columns. One for frequency and the other for the data we need to organize. The title and the column names should be properly labeled by the students to make the table more visually and structurally clear.

Mistake 5

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Incorrect ordering of data

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Kids should categorize the data and sort the intervals in ascending order for accuracy. Sometimes, they mistakenly order the intervals like 45 - 55, 60 - 76, 50 - 40, and so on.

arrow-right
Ray Thinking Deeply About Math Problems

FAQs on Frequency Distribution Table

1.What do you mean by frequency distribution table?

Math FAQ Answers Dropdown Arrow

2.Define the difference between grouped and ungrouped frequency distribution.

Math FAQ Answers Dropdown Arrow

3.What are the different methods to represent a frequency distribution table?

Math FAQ Answers Dropdown Arrow

4.Figure out the various types of frequency distribution tables.

Math FAQ Answers Dropdown Arrow
Math Teacher Background Image
Math Teacher Image

Jaipreet Kour Wazir

About the Author

Jaipreet Kour Wazir is a data wizard with over 5 years of expertise in simplifying complex data concepts. From crunching numbers to crafting insightful visualizations, she turns raw data into compelling stories. Her journey from analytics to education ref

Max, the Girl Character from BrightChamps

Fun Fact

: She compares datasets to puzzle games—the more you play with them, the clearer the picture becomes!

INDONESIA - Axa Tower 45th floor, JL prof. Dr Satrio Kav. 18, Kel. Karet Kuningan, Kec. Setiabudi, Kota Adm. Jakarta Selatan, Prov. DKI Jakarta
INDIA - H.No. 8-2-699/1, SyNo. 346, Rd No. 12, Banjara Hills, Hyderabad, Telangana - 500034
SINGAPORE - 60 Paya Lebar Road #05-16, Paya Lebar Square, Singapore (409051)
USA - 251, Little Falls Drive, Wilmington, Delaware 19808
VIETNAM (Office 1) - Hung Vuong Building, 670 Ba Thang Hai, ward 14, district 10, Ho Chi Minh City
VIETNAM (Office 2) - 143 Nguyễn Thị Thập, Khu đô thị Him Lam, Quận 7, Thành phố Hồ Chí Minh 700000, Vietnam
Dubai - BrightChamps, 8W building 5th Floor, DAFZ, Dubai, United Arab Emirates
UK - Ground floor, Redwood House, Brotherswood Court, Almondsbury Business Park, Bristol, BS32 4QW, United Kingdom