Albert Teen
Probability & Statistics

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Cumulative Frequency Diagrams

# Cumulative Frequency Diagrams

### Cumulative Frequency Diagrams

Cumulative frequency diagrams are a visual way to represent the running total of items or values.

Cumulative frequency diagrams are used to represent a “running total” of items or values. They are particularly useful for estimating values such as the median or interquartile range from data collected in group intervals.

Cumulative frequency is a measure of...

1

A group of 40 students take part in a jigsaw puzzle competition

Information on the time it took for students to complete a puzzle is given in the table.

2

Before drawing a diagram, we should work out the cumulative frequency

The cumulative frequency can be found by adding together the current frequency and each of the previous frequency values.

3

We can see some cumulative frequencies filled out in the table

For the interval $5 , the cumulative frequency is $4+7=11$. Similarly, at $10, the cumulative frequency is $4+7+12=23$.

4

What is the cumulative frequency for $15?

5

The cumulative frequency at $15 is 33

We can add 10 onto the previous cumulative frequency value: $23+10=33$.

6

What is the cumulative frequency at $20?

7

At $20, the cumulative frequency is 40

We add 7 to the previous cumulative frequency value: $33+7=40$

8

To translate this to a diagram, we need to generate points

On our cumulative frequency diagram, we will plot the cumulative frequency on the y-axis and the time taken along the x-axis.

9

To generate coordinates, use the upper bound of each interval

For the interval $0, the upper bound of the interval is 5, while the cumulative frequency is 4. Therefore, the coordinate is $(5,4)$. We can see this repeated for the other two coordinates.

10

What is the coordinate for the interval $20?

11

The coordinate should be $(25,40)$

The upper bound of the interval is 25 (x-coordinate), while the cumulative frequency is 40 (y-coordinate).

12

What is the coordinate for the interval $10?

13

The coordinate should be $(15,23)$

The upper bound of the interval is 15 (x-coordinate), while the cumulative frequency is 23 (x-coordinate).

When drawing a cumulative frequency table from a dataset containing intervals, the x-coordinate for the interval should be the...