Albert Teen YOU ARE LEARNING:  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... 