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      Constructing a cumulative frequency graph

      Lesson details

      Learning outcome

      I can construct a cumulative frequency graph.

      Key learning points

      1. A cumulative frequency graph can be drawn from a frequency table
      2. It can be easier to create another column to sum the frequencies
      3. Cumulative frequency graphs are drawn as smooth curves

      Keywords

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

      Common misconception

      Plotting the midpoint of the class against the cumulative frequency.

      Ensure that the pupils are clear that each cumulative frequency includes all values up to the upper boundary of each group.

      Teacher tip

      Collect a continuous data set from the class, e.g. heights, handspan and they can then draw a cumulative frequency graph of this data.

      Licence

      This content is © Oak National Academy Limited (2025), 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.
      This is a table showing the colours of some cars in a car park. Which of the following could be a title for the third column?

      An image in a quiz
      Angle
      Correct answer: Frequency
      Tally
      Number

      Q2.
      This table shows the colours of 100 cars in a car park. How many are white?

      An image in a quiz
      Correct Answer: 29

      Q3.
      What is the upper boundary of this group? $$20 < x \leq40$$

      Correct Answer: 40

      Q4.
      Which two numbers are covered in this table?

      An image in a quiz
      41 and 60
      41 and 59
      40 and 59
      Correct answer: 40 and 60

      Q5.
      What are the coordinates of point A? (Remember to write your answer using brackets.)

      An image in a quiz
      Correct Answer: (10, 4), (10,4), (10 , 4)

      Q6.
      What are the coordinates of point B? (Remember to write your answer using brackets.)

      An image in a quiz
      Correct Answer: (50, 30), (50, 30), (50 , 30)

      6 Questions

      Q1.
      frequency is the total of all frequencies up to a defined class. It is the 'running total' of frequencies.

      Correct Answer: Cumulative, cumulative

      Q2.
      What is the next cumulative frequency?

      An image in a quiz
      Correct Answer: 45

      Q3.
      What is the missing cumulative frequency?

      An image in a quiz
      Correct Answer: 77

      Q4.
      When plotting the points on a cumulative frequency graph you plot the cumulative frequency against what?

      Lower boundary of the group
      Mid-point of the group
      Correct answer: Upper boundary of the group
      Any point in the group

      Q5.
      After the points have been plotted what should you do next?

      Draw a line of best fit
      Do not join the points
      Join the points with a ruler
      Correct answer: Join the points with a smooth curve

      Q6.
      What coordinates should be plotted for the third point?

      An image in a quiz
      (45, 32)
      (30, 77)
      (45, 77)
      (50, 32)
      Correct answer: (50, 77)

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