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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...
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.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/TZ8adOUSCdAfzp3Rk2ag.png)
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.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/TZ8adOUSCdAfzp3Rk2ag.png)
We can see some cumulative frequencies filled out in the table
For the interval 5<x≤10, the cumulative frequency is 4+7=11. Similarly, at 10<x≤15, the cumulative frequency is 4+7+12=23.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/OJkFUljGSiuMOZdBd7Uf.png)
What is the cumulative frequency for 15<x≤20?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/OJkFUljGSiuMOZdBd7Uf.png)
The cumulative frequency at 15<x≤20 is 33
We can add 10 onto the previous cumulative frequency value: 23+10=33.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/fvAdOE5qTja3QxwH0ibY.png)
What is the cumulative frequency at 20<x≤25?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/fvAdOE5qTja3QxwH0ibY.png)
At 20<x≤25, the cumulative frequency is 40
We add 7 to the previous cumulative frequency value: 33+7=40
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/z5PZ4MSS5KyUiyPtGQGY.png)
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.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/z5PZ4MSS5KyUiyPtGQGY.png)
To generate coordinates, use the upper bound of each interval
For the interval 0<x≤5, 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.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/lU6wUvWVSGgCyaaoDUsN.png)
What is the coordinate for the interval 20<x≤25?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/lU6wUvWVSGgCyaaoDUsN.png)
The coordinate should be (25,40)
The upper bound of the interval is 25 (x-coordinate), while the cumulative frequency is 40 (y-coordinate).
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/5zSjImfRKSYTs9zFrI7g.png)
What is the coordinate for the interval 10<x≤15?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/5zSjImfRKSYTs9zFrI7g.png)
The coordinate should be (15,23)
The upper bound of the interval is 15 (x-coordinate), while the cumulative frequency is 23 (x-coordinate).
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/B9xkorxT6WgIhpROTwjC.png)
When drawing a cumulative frequency table from a dataset containing intervals, the x-coordinate for the interval should be the...