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The cumulative sum of the frequency of a certain class interval, referred to as the cumulative frequency, is the total number of observations of this class interval and all the class intervals that precede it.

The first cumulative frequency is equal to the first frequency.
The second cumulative frequency is equal to the sum of the second frequency and the first cumulative frequency.
The third cumulative frequency is equal to the sum of the third frequency and the second cumulative frequency, and so on until we get to the n frequency which is equal to the sum of the first end frequencies.

For example:

The students of a certain school were measured in height to the nearest centimeter. The results are displayed in the table below:

In order to find x, we need to add the second frequency and the first cumulative frequency:

x = 56 + 10

x = 66

Now, to find y, we know that y + 161 (cumulative frequency) = 281.
Thus:

y = 281 - 161

y = 120

Now try:

The length of 50 rods are shown in the table below. Find the cumulative frequency of each length:

Solution:

The end cumulative frequency which is 50, is equal to the number of rods.

Resources:
https://www.wyzant.com/resources/lessons/math/statistics_and_probability/averages/cumulative_frequency_percentiles_and_quartiles

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