# Types of Frequency Distribution

• Unprocessed and unsorted data is a waste provides no information. Frequency Distribution is a way to sort data in a manner so that it may give the desired information.
• Frequency implies a number of repetitions of a certain event e.g. Ram deposit his insurance premium on a monthly basis, so the frequency of payments made by Ram in a year towards insurance is 12, similarly, frequency of Monday in a week is 1. Distribution means sorting/distributing data in a particular manner.
• Hence Frequency Distribution implies sorting or distributing data based on its frequency.

## Methods of frequency distribution

• There are two major ways in which frequency distribution is done:
• Discrete Frequency Distribution: It measures the frequency of a discrete value.
• Continuous Frequency distribution: It measures the frequency of a value range.

#### Example 1:

• Discrete Frequency Distribution: Number of marks obtained by each student of a class, is an example of Discrete Frequency Distribution.
Marks Obtained Number of Students
2 10
4 12
6 15
8 8
10 5

#### Example 2:

• Continuous Value Frequency Distribution: Consolidating the above data of marks based on a range of marks, is an example of Continuous Value Distribution. The range is continuous, this implies that the end of one range is the starting point of the next range.
Score Range Number of Students
0-2 10
2-4 22
4-6 27
6-8 23
8-10 13

## Creating a Frequency Distribution:

#### Example. 3:

2,4,5,6,2,4,7,8,4,5,9,6,10,10,9,10 are the marks obtained by students of a class, create a frequency distribution from the same.
• Sort the data in ascending/descending order
• 2,2,4,4,4,5,5,6,6,7,8,9,9,10,10,10
• Find out the High-Low Range: 2 is lowest and 10 is highest
• Count and note the frequency of discrete value or a range in tabular form as shown below

### Discrete Frequency Distribution

Discrete Frequency Distribution
Marks No. of Students
2 2
4 3
5 2
6 2
7 1
8 1
9 2
10 3

### Continuous Value Frequency Distribution

Continuous Value Frequency Distribution
Marks Range No. of Students
0-2 2
3- 5 5
6-8 4
9-10 5

## Other Important Types of Frequency Distribution

### Relative Frequency:

• It implies the frequency of a certain value with respect to the total frequency of all the elements in the data set. It is calculated by dividing by the frequency of value by the total frequency of all elements.
• Considering the above example again, the relative frequency of the number of students who obtained 2 marks is calculated by dividing No. of Students who got 2 marks by a total number of students. Refer to the following table.
Total Number of Students = 16
Sum of All Relative Frequency = 1
Marks No. of Students Relative Frequency
2 2 0.13
4 3 0.19
5 2 0.13
6 2 0.13
7 1 0.06
8 1 0.06
9 2 0.13
10 3 0.19
• It should be noted that sum of all Relative Frequency should always be 1.

### Percentage Frequency Distribution

• It is the measurement that shows how much space the frequency of an element is holding in a data set. It is obtained by multiplying the Relative Frequency by 100. Consider the following table.
• It should be noted that sum of all percentage frequency should be 100.
Marks No. of Students Relative Frequency Percentage Frequency
2 2 0.13 12.5
4 3 0.19 18.75
5 2 0.13 12.5
6 2 0.13 12.5
7 1 0.06 6.25
8 1 0.06 6.25
9 2 0.13 12.5
10 3 0.19 18.75

### Cumulative or Less than Cumulative Frequency Distribution

• It is the sum of a frequency and all frequencies before it. For e.g. in the above table Cumulative Frequency of all students who got 6 marks will be the sum of students who got 6 marks and all students who got less than 6 marks. Please refer to the table below:
Marks No. of Students Relative Frequency Percentage Frequency Cumulative Frequency
2 2 0.13 12.5 2
4 3 0.19 18.75 5
5 2 0.13 12.5 7
6 2 0.13 12.5 9
7 1 0.06 6.25 10
8 1 0.06 6.25 11
9 2 0.13 12.5 13
10 3 0.19 18.75 16
• Referring to the above table, it is very clearly visible that the cumulative frequency of the last element must be equal to the total number of elements in the data set.
• Cumulative Frequency provides a sum of referred data as well as all occurrences up to that data i.e. in the above table cumulative frequency of students who obtained marks is the sum of all candidates who got up to 6 marks i.e. from 0 to 6.

### Cumulative More than Frequency

• It is just the opposite of less than cumulative frequency, it is the difference between the total sum of all frequency’s upper element frequency. Cumulative More than Frequency of all students who got 6 marks will be the difference between total frequency and a total of students who got less than 6 marks. Consider the following table:
Marks No. of Students Relative Frequency Percentage Frequency Cumulative Frequency Cumulative More than Frequency
2 2 0.13 12.5 2 16
4 3 0.19 18.75 5 14
5 2 0.13 12.5 7 11
6 2 0.13 12.5 9 9
7 1 0.06 6.25 10 7
8 1 0.06 6.25 11 6
9 2 0.13 12.5 13 5
10 3 0.19 18.75 16 3

### Cumulative Relative Frequency

• It is obtained by dividing cumulative frequency by total frequency. E.g. relative frequency of a number of students who scored 4 marks will be obtained by dividing cumulative frequency i.e. 5 by total frequency i.e. 16 Consider the following table:
Marks No. of Students Relative Frequency Percentage Frequency Cumulative Frequency Cumulative More than Frequency Cumulative Relative Frequency
2 2 0.13 12.5 2 16 0.086956522
4 3 0.19 18.75 5 14 0.217391304
5 2 0.13 12.5 7 11 0.304347826
6 2 0.13 12.5 9 9 0.391304348
7 1 0.06 6.25 10 7 0.434782609
8 1 0.06 6.25 11 6 0.47826087
9 2 0.13 12.5 13 5 0.565217391
10 3 0.19 18.75 16 3 0.695652174 