New
New
Year 11
Higher

Interpreting a cumulative frequency graph

I can interpret a cumulative frequency graph.

New
New
Year 11
Higher

Interpreting a cumulative frequency graph

I can interpret a cumulative frequency graph.

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Lesson details

Key learning points

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

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).

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.

Carefully check that pupils are using a smooth curve to join their points rather than straight line segments.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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6 Questions

Q1.
Cumulative frequency is the total of all frequencies up to a defined class. It is the ' total' of frequencies.
Correct Answer: running
Q2.
What is the next cumulative frequency?
An image in a quiz
Correct Answer: 36
Q3.
What is the missing cumulative frequency?
An image in a quiz
Correct Answer: 74
Q4.
Which of the following is not correct when drawing a cumulative frequency graph?
Join the points with a smooth curve
Correct answer: Plot the cumulative frequency with the mid-point of the group
Plot the cumulative frequency on the vertical axis
Correct answer: Join the points with a ruler
Q5.
What coordinates should be plotted for the second point?
An image in a quiz
(30, 36)
(35, 24)
(40, 24)
(35, 36)
Correct answer: (40, 36)
Q6.
What coordinates should be plotted for the third point?
An image in a quiz
(40, 62)
(45, 74)
(50, 38)
(45, 38)
Correct answer: (50, 74)

6 Questions

Q1.
The third quartile $$Q_3$$ is the .
Correct Answer: upper quartile
Q2.
Use this graph to estimate the median.
An image in a quiz
10
15
Correct answer: 22
28
29
Q3.
Use this graph to estimate the lower quartile.
An image in a quiz
5
7.5
11
Correct answer: 16
21
Q4.
Use this graph to estimate the upper quartile.
An image in a quiz
15
22
Correct answer: 28
30
32
Q5.
35% of people score or less.
An image in a quiz
Correct Answer: 12
Q6.
Any pupil scoring over 20 marks gets a certificate. How many certificates are given out?
An image in a quiz
Correct Answer: 2