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<center>[Source](https://i.ytimg.com/vi/l15vCWg5VDg/maxresdefault.jpg)</center>

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.
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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:
<center>https://imgoat.com/uploads/c8349cc726/44699.PNG</center>
In order to find *x*, we need to add the second frequency and the first cumulative frequency:
#### *x* = 56 + 10
#### *x* = 66
<br>
Now, to find *y*, we know that *y* + 161 (cumulative frequency) = 281.
Thus:
#### *y* = 281 - 161
#### *y* = 120
<center>https://imgoat.com/uploads/c8349cc726/44700.PNG</center>
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# Now try:
## The length of 50 rods are shown in the table below.  Find the cumulative frequency of each length:
<center>https://imgoat.com/uploads/c8349cc726/44702.PNG</center>
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# Solution:
<center>https://imgoat.com/uploads/c8349cc726/44703.PNG</center>
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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