# Find and Interpret Cumulative Frequency

In this worksheet, students will find and interpret cumulative frequencies of data sets.

Key stage:  KS 3

Curriculum topic:   Statistics

Curriculum subtopic:   Understand Variables, Representation, Measures and Spread

Difficulty level:

#### Worksheet Overview

What does it mean when you accumulate something?

It means you collect or gather something, typically over a period of time!

What could cumulative frequency mean then?

Well, we know frequency tells us how many times something occurred.

When we have cumulative frequency (c.f. for short), we just accumulate all the frequencies up to that point.

Let's have a look at an example to understand this better:

14 women were asked their shoe size and these were the answers:

9, 7, 8, 8, 8, 6, 8, 7, 8, 6, 7, 7, 8, 9, 8

The data was organised into a frequency table:

Shoe Size Frequency
6 2
7 4
8 6
9 2

If we wanted to find the cumulative frequency for shoe size 7, we find the number of women who have the shoe size of 7 or less.

Since 2 women wear the size 6, 4 wear size 7 and there are no other sizes smaller than or equal to 7 in our data set, the cumulative frequency for shoe size 7 is:

2 + 4 = 6

Can you see how we accumulated all the frequencies up to 7?!

We often create a new column in the frequency table to find the cumulative frequencies:

Shoe Size Frequency Cumulative frequency
6 2 2
7 4 2 + 4 = 6
8 6 6 + 6 = 12
9 2 12 + 2 = 14

To find the cumulative frequency, we simply add all the frequencies up to that row (including it!).

The meaning of cumulative frequency is how many data points there are equal to or less than certain value.

For example, in the above table, we can see that 12 women wear size 8 or smaller.

Ready for some questions?!

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