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4024/22 May/Jun 2022, Question 5: Estimating the Mean for Grouped Data

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 10 marks

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The question, in short

Using a grouped frequency table of puzzle completion times, find a cumulative count and estimate the mean; then use a cumulative frequency curve to complete a table, estimate the median, and find a value k.

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

Part (ai) · 1 mark

Find how many students took 2 minutes 20 seconds or less, using the grouped frequency table.

  1. 12 minutes 20 seconds = 140 seconds
  2. 213 + 26 = 39

Answer39

Part (aii) · 3 marks

Estimate the mean completion time in seconds from the grouped frequency table.

  1. 1Midpoints: 100, 130, 145, 195
  2. 2Σfx = 13 × 100 + 26 × 130 + 27 × 145 + 24 × 195 = 1300 + 3380 + 3915 + 4680 = 13 275
  3. 3Σf = 13 + 26 + 27 + 24 = 90
  4. 4Mean = 13 275 ÷ 90 = 147.5 s

Answer147.5 or 147 1/2

Part (bi) · 2 marks

Use the cumulative frequency curve to fill in the missing frequencies for the adult time intervals.

  1. 1Read cumulative frequencies at t = 100, 150, 200, 250, 300: 8, 30, 66, 112, 120
  2. 2Frequencies: 30 − 8 = 22, 66 − 30 = 36, 112 − 66 = 46, 120 − 112 = 8
  3. 322, 36, 46, 8

Answer| Time (t seconds) | 100 < t ≤ 150 | 150 < t ≤ 200 | 200 < t ≤ 250 | 250 < t ≤ 300 | | Frequency | 22 | 36 | 46 | 8 | or | Frequency | 22 | 35 | 47 | 8 |

Part (bii) · 1 mark

Use the cumulative frequency curve to estimate the median completion time.

  1. 1Total = 120, so the median is at cumulative frequency 60
  2. 2Read across from 60 to the curve and down
  3. 3Median ≈ 195 s

Answer192.5 to 197.5

Part (biii) · 3 marks

Given 55% of adults took between 125 seconds and k seconds, use the curve to find k.

  1. 155% of 120 = 66 adults
  2. 2Cumulative frequency at t = 125 is 18
  3. 318 + 66 = 84; read across from 84 to the curve and down
  4. 4k ≈ 215

Answer212.5 to 217.5

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Also searched as: 4024/22/M/J/22 · 4024_s22_qp_22 · 4024 s22 22 · question 5.
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