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4MA1/1F Jan 2021, Question 18: Estimating the Mean for Grouped Data

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1F (Foundation) · Calculator · 5 marks

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The question, in short

From a grouped frequency table of 80 motorbike speeds in km/h, identify the modal class and estimate the mean speed to 3 significant figures.

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

Part (a) · 1 mark

State which speed class interval has the highest frequency.

  1. 1The modal class is the class with the highest frequency.
  2. 2The frequencies are 10, 16, 19, 23 and 12, and the largest of these is 23.
  3. 3The modal class is 70 < s ≤ 80

Answer70 < s ≤ 80

Part (b) · 4 marks

Use class midpoints and frequencies to estimate the mean speed, giving the answer to 3 significant figures.

  1. 1Use the mid-value of each class: 45, 55, 65, 75, 85
  2. 245 × 10 = 450, 55 × 16 = 880, 65 × 19 = 1235, 75 × 23 = 1725, 85 × 12 = 1020
  3. 3Total of the products = 450 + 880 + 1235 + 1725 + 1020 = 5310
  4. 4Estimated mean = 5310 ÷ 80 = 66.375
  5. 5The estimate for the mean speed is 66.4 kilometres per hour (to 3 significant figures).

Answer66.4

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