Types of Frequency Distribution

There are four types of frequency distribution:

• Grouped Frequency Distribution
• Ungrouped Frequency Distribution
• Relative Frequency Distribution
• Cumulative Frequency Distribution

Grouped Frequency Distribution

In Grouped Frequency Distribution observations are divided between different intervals known as class intervals and then their frequencies are counted for each class interval. This Frequency Distribution is used mostly when the data set is very large.

Example: Make the Frequency Distribution Table for the ungrouped data given as follows:

23, 27, 21, 14, 43, 37, 38, 41, 55, 11, 35, 15, 21, 24, 57, 35, 29, 10, 39, 42, 27, 17, 45, 52, 31, 36, 39, 38, 43, 46, 32, 37, 25

Solution:

As there are observations in between 10 and 57, we can choose class intervals as 10-20, 20-30, 30-40, 40-50, and 50-60. In these class intervals all the observations are covered and for each interval there are different frequency which we can count for each interval.

Thus, the Frequency Distribution Table for the given data is as follows:

Ungrouped Frequency Distribution

In Ungrouped Frequency Distribution, all distinct observations are mentioned and counted individually. This Frequency Distribution is often used when the given dataset is small.

Example: Make the Frequency Distribution Table for the ungrouped data given as follows:

10, 20, 15, 25, 30, 10, 15, 10, 25, 20, 15, 10, 30, 25

Solution:

As unique observations in the given data are only 10, 15, 20, 25, and 30 with each having a different frequency.

Thus the Frequency Distribution Table of the given data is as follows:

Relative Frequency Distribution

This distribution displays the proportion or percentage of observations in each interval or class. It is useful for comparing different data sets or for analyzing the distribution of data within a set.

Relative Frequency is given by:

Relative Frequency = (Frequency of Event)/(Total Number of Events)

Example: Make the Relative Frequency Distribution Table for the following data:

Solution:

To Create the Relative Frequency Distribution table, we need to calculate Relative Frequency for each class interval. Thus Relative Frequency Distribution table is given as follows:

Score Range	Frequency	Relative Frequency
0-20	5	5/50 = 0.10
21-40	10	10/50 = 0.20
41-60	20	20/50 = 0.40
61-80	10	10/50 = 0.20
81-100	5	5/50 = 0.10
Total	50	1.00

Cumulative Frequency Distribution

Cumulative frequency is defined as the sum of all the frequencies in the previous values or intervals up to the current one. The frequency distributions which represent the frequency distributions using cumulative frequencies are called cumulative frequency distributions. There are two types of cumulative frequency distributions:

• Less than Type: We sum all the frequencies before the current interval.
• More than Type: We sum all the frequencies after the current interval.

Check:

• Cumulative Frequency
• How to Calculate Cumulative Frequency table in Excel

Let’s see how to represent a cumulative frequency distribution through an example, 

Example: The table below gives the values of runs scored by Virat Kohli in the last 25 T-20 matches. Represent the data in the form of less-than-type cumulative frequency distribution: 

Solution: 

Since there are a lot of distinct values, we’ll express this in the form of grouped distributions with intervals like 0-10, 10-20 and so. First let’s represent the data in the form of grouped frequency distribution. 

Runs	Frequency
0-10	2
10-20	2
20-30	1
30-40	4
40-50	4
50-60	5
60-70	1
70-80	3
80-90	2
90-100	1

Now we will convert this frequency distribution into cumulative frequency distribution by summing up the values of current interval and all the previous intervals. 

Runs scored by Virat Kohli	Cumulative Frequency
Less than 10	2
Less than 20	4
Less than 30	5
Less than 40	9
Less than 50	13
Less than 60	18
Less than 70	19
Less than 80	22
Less than 90	24
Less than 100	25

This table represents the cumulative frequency distribution of less than type. 

Runs scored by Virat Kohli	Cumulative Frequency
More than 0	25
More than 10	23
More than 20	21
More than 30	20
More than 40	16
More than 50	12
More than 60	7
More than 70	6
More than 80	3
More than 90	1

This table represents the cumulative frequency distribution of more than type.

We can plot both the type of cumulative frequency distribution to make the Cumulative Frequency Curve.

Frequency Distribution is a tool in statistics that helps us organize the data and also helps us reach meaningful conclusions. It tells us how often any specific values occur in the dataset.

A frequency distribution represents the pattern of how frequently each value of a variable appears in a dataset. It shows the number of occurrences for each possible value within the dataset.

Let’s learn about Frequency Distribution including its definition, graphs, solved examples, and frequency distribution table in detail.