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4024/21 Oct/Nov 2021, Question 2: Histograms (Unequal Class Intervals)

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 9 marks

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The question, in short

Use a frequency table for 80 gym members' weekly class counts and a histogram of visit times to find averages, a pie chart angle, sample size and check a claim.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (ai) · 1 mark

Find the mode of the number of classes attended.

  1. 1Highest frequency is 29, so mode = 1

Answer1

Part (aii) · 1 mark

Find the median number of classes attended.

  1. 1Median is between the 40th and 41st values
  2. 2Cumulative frequencies: 10, 39, 65 → both are 2
  3. 3Median = 2

Answer2

Part (aiii) · 2 marks

Calculate the pie chart angle for members attending 5 classes.

  1. 15 classes: frequency 2 out of 80 members
  2. 2Angle = 2/80 × 360 = 9°

Answer9

Part (bi) · 3 marks

Given 30 members spent 30 to 60 minutes, calculate the total number surveyed.

  1. 1Frequency = frequency density × class width
  2. 20.6 × 30 + 1 × 30 + 4.4 × 15 + 1.6 × 15 + 0.4 × 30
  3. 3= 18 + 30 + 66 + 24 + 12 = 150

Answer150

Part (bii) · 2 marks

Decide whether one tenth spent longer than 1 1/2 hours, justifying with histogram frequencies.

  1. 11 1/2 hours = 90 minutes: longer than 90 min = 0.4 × 30 = 12 members
  2. 21/10 of 150 = 15
  3. 312 ≠ 15, so he is wrong

Answer1/10 is 15 and 12 spend more than 90 minutes, so he is wrong

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