In this article we will learn how to calculate cumulative frequency(cf) but before that, lets define frequency. Frequency is the number of times something happens within a particular period.
Cumulative means increasing or growing by accumulation or successive additions. Therefore, cumulative frequency is the total of a frequency and all frequencies so far in a frequency distribution.
Types of Cumulative Frequency.
There are two types of cumulative frequency i.e lesser than and greater than cumulative frequency.
Lesser Than Cumulative Frequency.
Lesser than cumulative frequency is obtained by adding successively the frequencies of all the previous classes including the class against which it is written. The cumulate starts from the lowest to the highest size.
Greater Than Cumulative Frequency.
Greater than cumulative frequency is obtained by finding the cumulative total of frequencies starting from the highest to the lowest class. It is also called more than type cumulative frequency.
How to Calculate Cumulative Frequency.
Example:
The frequency distribution table below records number of plates with their colors.
| Color of plate | Number (Frequency) |
| Red | 12 |
| Blue | 8 |
| Violet | 15 |
| Indigo | 20 |
The first cumulative frequency is the same as the first frequency, as you just add a zero to the frequency.
To calculate cf, we add the first frequency to the second frequency, then add the third frequency to the result and the process continues.
| Color of plate | Number (frequency) | Cumulative frequency |
| Red | 12 | 12 |
| Blue | 8 | 20 |
| Violet | 15 | 35 |
| Indigo | 20 | 55 |
The cumulative frequency in the last row is the same as the total sum of frequencies.
Example 2:
