1274 LearnersLast updated on June 5th, 2025
Frequency Distribution
Frequency distribution is a method in statistics that is used to organize and summarize data by showing how often each value in a range of values appears in a dataset. It helps us in identifying patterns, trends, and distributions within data, which makes it easier to analyze and interpret. Let us now see more about frequency distributions and how they are calculated.
What is a frequency distribution?
A frequency distribution is a way of organizing and representing data to show how typically each value or range of values occurs in a data set. It helps in summarizing large amounts of data and identifying patterns or trends.
The key takeaways are as follows:
- Organizes data by grouping the similar data together
- Can be grouped or ungrouped, depending on the size of the data set.
- Used in statistics, research, and probability to analyze trends.
- Helps visualize data using tables, graphs, or histograms.
- Essential for calculating probabilities, percentiles, and cumulative frequencies.
To calculate a frequency distribution, we use the following formula:
Relative frequency (%) = (Class Frequency / Total frequency x 100.
What are the Types of Frequency Distribution
There are four types of frequency distribution, which are listed below:
Ungrouped Frequency Distribution:
Data is presented in a list or a table without being grouped into intervals. For example, test scores of students:
| Score | Frequency |
| 45 | 1 |
| 50 | 2 |
| 55 | 2 |
| 60 | 2 |
| 65 | 1 |
It is used for small datasets with distinct values that do not need grouping.
Grouped Frequency Distribution:
Data is divided into intervals or class groups to make it easier to analyze. For example:
| Class Interval | Frequency |
| 40 – 49 | 1 |
| 50 – 59 | 4 |
| 60 – 69 | 3 |
| 70 – 79 | 2 |
| 80 – 89 | 3 |
We use it when the data set is large and individual values can be grouped into meaningful ranges.
Cumulative Frequency Distribution:
Shows the sum of frequencies up to a certain class interval. For example:
| Class Interval | Frequency | Cumulative Frequency |
| 40 – 49 | 1 | 1 |
| 50 – 59 | 4 | 5 |
| 60–69 | 3 | 8 |
| 70–79 | 2 | 10 |
We use it when analyzing percentiles, medians, or data trends over time.
Relative Frequency Distribution:
Expresses frequency as a percentage of the total number of observations. The formula used is:
Relative frequency = class frequency/total frequency x 100
For example,
| Class Interval | Frequency | Relative Frequency |
| 40 – 49 | 1 | 6.67% |
| 50 – 59 | 4 | 26.67% |
| 60–69 | 3 | 20% |
| 70–79 | 2 | 13.33% |
We use it to compare distributions with total frequencies or for probability based studies.
How to make a frequency table
There are two ways to make a frequency table, that is for an ungrouped data and for a grouped data. Let us see what steps are involved to make frequency tables for both types of data:
For Ungrouped Frequency:
To create an ungrouped frequency table, we have to follow the following steps:
Step 1: Create a table with two columns and rows. Label the first column using the variable name and the second column named as frequency.
Step 2: Then we must count the frequencies. Frequencies are the number of times each value occurs. Enter the frequencies in the frequency column.
For Grouped Data:
The following steps must be followed in order to create a table for grouped data:
Step 1: First we must divide the variable into class intervals. To do that, we need to calculate the range by subtracting the lowest value from the highest value. Then we need to find the class width. To calculate the width we have to use the following formula:
Width = range /√sample size
Then we have to calculate the class intervals. The observations in a class interval are greater than or equal to the lower limit and less than the upper limit.
Step 2: We have to create a table with the class interval, and the frequency.
Step 3: Then we have to count the frequency. Frequencies are the number of times each value occurs. Enter the frequencies in the frequency column.
Real-life applications on Frequency Distributions
The frequency distribution tables have numerous applications across various fields. Let us explore how the frequency table is used in different areas:
Education and Academics:
We use frequency tables in education and academics, where schools use frequency tables to track students’ grades and assess overall performance, and teachers use them to maintain frequency tables to analyze student attendance patterns over a semester.
Business and Sales:
In business and sales, frequency tables are widely used to track how often certain products are purchased in an inventory. Companies use the frequency table to assess sales trends over different periods.
Healthcare and Medicine:
We use frequency tables in healthcare and medicine, where hospitals maintain records of how frequently different diseases occur in patients, and pharmaceutical companies track the frequency of medicine prescriptions to understand demand.
Common Mistakes and How to Avoid Them in Frequency Distributions
Students tend to make some mistakes while making frequency tables. Let us now see the different types of mistakes students make while creating frequency tables and their solutions:
Mistake 1
Inconsistent Class Intervals
Students should ensure that all class intervals are of the same width. If the class intervals are not uniform, then it becomes a hassle to solve problems using the frequency tables.
Solved examples on Frequency Distribution
Problem 1
Given the data set: 3, 5, 3, 7, 9, 3, 5, 9, construct a frequency table showing the number of times each number appears.
| Value | Frequency |
| 3 | 3 |
| 5 | 2 |
| 7 | 1 |
| 9 | 2 |
Explanation
Identify unique values: 3, 5, 7, 9
Count Occurrences:
3 appears 3 times
5 appears 2 times
7 appears 1 time
9 appears 2 times
Create the table.
Problem 2
For the dataset: 2, 4, 2, 3, 2, 4, 5, 3, 4, 2, construct a frequency table showing both absolute frequency and relative frequency (in percentages).
| Value | Frequency | Relative Frequency |
| 2 | 4 | 40% |
| 3 | 2 | 20% |
| 4 | 3 | 30% |
| 5 | 1 | 10% |
Explanation
Unique values: 2, 3, 4, 5.
Count Frequencies:
2 appears 4 times.
3 appears 2 times
4 appears 3 times
5 appears 1 time
Total data points: 10
Calculate relative frequency:
2: 4/10 x 100 = 40%
3: 2/10 x 100 = 20%
4: 3/10 x 100 = 30%
5: 1/10 x 100 = 10%
Construct the table.
Problem 3
For the exam scores: 55, 60, 70, 55, 80, 90, 60, 70, 80, 90, construct a frequency table that includes cumulative frequency.
| Score | Frequency | Cumulative Frequency |
| 55 | 2 | 2 |
| 60 | 2 | 4 |
| 70 | 2 | 6 |
| 80 | 2 | 8 |
| 90 | 2 | 10 |
Explanation
Unique Scores: 55, 60, 70, 80, 90.
Count Frequencies:
55: 2 times
60: 2 times
70: 2 times
80: 2 times
90: 2 times
Cumulative Frequency Calculation:
55: 2
60: 2 + 2 = 4
70: 4 + 2 = 6
80: 6 + 2 = 8
90: 8 + 2 = 10
Construct a table.
Problem 4
Give the color responses: Red, Blue, Green, Red, Blue, Yellow, Red, Blue, Green, Red, construct a frequency table.
| Color | Frequency |
| Red | 4 |
| Blue | 3 |
| Green | 2 |
| Yellow | 1 |
Explanation
Identify the Unique Colors: Red, Blue, Green, Yellow
Count Frequencies:
Red: 4
Blue: 3
Green: 2
Yellow: 1
Construct the table.
Problem 5
For the exam grades: 78, 82, 90, 78, 85, 82, 90, 95, 78, 85, build a table that includes absolute frequency, relative frequency (percentages), and cumulative frequency.
| Grade | Frequency | Relative Frequency | Cumulative Frequency |
| 78 | 3 | 30% | 3 |
| 82 | 2 | 20% | 5 |
| 85 | 2 | 20% | 7 |
| 90 | 2 | 20% | 9 |
| 95 | 1 | 10% | 10 |
Explanation
Unique Grades: 78, 82, 85, 90, 95
Count Frequencies:
78: 3
82: 2
85: 1
90: 2
95: 1
Total Data Points: 10
Calculate Relative Frequencies:
78: 30%
82: 20%
85: 20%
90: 20%
95: 10%
Cumulative Frequency:
78: 3
82: 3 + 2 = 5
85: 5 + 2 = 7
90: 7 + 2 = 9
95: 9 + 1 = 10.
Construct the table.
FAQs on Frequency Distribution
1.What is a frequency distribution?
2.What is the need do of a frequency table?
3.What is cumulative frequency?
4.When should you group data in a frequency table?
5.What insights can you gain from a frequency table?
6.How can children in Vietnam use numbers in everyday life to understand Frequency Distribution ?
7.What are some fun ways kids in Vietnam can practice Frequency Distribution with numbers?
8.What role do numbers and Frequency Distribution play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Frequency Distribution skills?
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
Fun Fact
: She compares datasets to puzzle games—the more you play with them, the clearer the picture becomes!
