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?!