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      Interpreting a cumulative frequency graph

      Lesson details

      Learning outcome

      I can interpret a cumulative frequency graph.

      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.

      Teacher tip

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

      Licence

      This content is © Oak National Academy Limited (2026), 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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      Prior knowledge starter quiz

      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

      To help you plan your 11 maths lesson on: Interpreting a cumulative frequency graph, download all teaching resources for free and adapt to suit your pupils' needs...