Interpreting a cumulative frequency graph | Maths | Quizalize & Oak National Academy

Starter quiz

Cumulative frequency is the total of all frequencies up to a defined class. It is the '______ total' of frequencies.

'running' ✓
What is the next cumulative frequency?

'36' ✓
What is the missing cumulative frequency?

'74' ✓
Which of the following is not correct when drawing a cumulative frequency graph?

Join the points with a smooth curve

Plot the cumulative frequency with the mid-point of the group ✓

Plot the cumulative frequency on the vertical axis

Join the points with a ruler ✓
What coordinates should be plotted for the second point?

(30, 36)

(35, 24)

(40, 24)

(35, 36)

(40, 36) ✓
What coordinates should be plotted for the third point?

(40, 62)

(45, 74)

(50, 38)

(45, 38)

(50, 74) ✓

Exit quiz

The third quartile $Q_3$ is the ______.

'upper quartile' ✓
Use this graph to estimate the median.

10

15

22 ✓

28

29
Use this graph to estimate the lower quartile.

5

7.5

11

16 ✓

21
Use this graph to estimate the upper quartile.

15

22

28 ✓

30

32
35% of people score ______ or less.

'12' ✓
Any pupil scoring over 20 marks gets a certificate. How many certificates are given out?

'2' ✓

Worksheet

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Lesson Details

Key learning points

A cumulative frequency has values read in the same way as a line graph
The median is the 50th percentile
The lower quartile is the 25th percentile
The upper quartile is the 75th percentile
Other percentiles can also be found

Common misconception

Using the highest value on the y-axis rather than the total frequency when calculating the values to read off for the lower quartile, median and upper quartile.

Ensure pupils understand that the total frequency must be used. A graph where the y-axis goes up to 100 and the total frequency is 40 can be used to highlight this. Then repeat with the same data, but with a graph where the y-axis goes up to 200.

Keywords

Percentile - A percentile is a value on a scale of 100 that indicates the percent of a distribution that is equal to or below it.
Lower quartile - The lower quartile is the value under which 25% of data points are found when they are arranged in increasing order. Also known as the first quartile (Q1).
Upper quartile - The upper quartile is the value under which 75% of data points are found when they are arranged in increasing order. Also known as the third quartile (Q3).