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0580/42 Feb/Mar 2021, Question 7: Estimating the Mean for Grouped Data

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 11 marks

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The question, in short

Use box-and-whisker plots of test marks and grouped frequency tables for plant heights and apple masses to find median, range, a possible mark, compare distributions, estimate a mean, and work with a histogram.

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

Part (ai) · 1 mark

Read the median mark from the box-and-whisker plot.

  1. 1Median is the line inside the box
  2. 2Median = 70

Answer70

Part (aii) · 1 mark

Calculate the range of marks from the box-and-whisker plot.

  1. 1Lowest = 12, highest = 90
  2. 2Range = 90 − 12 = 78

Answer78

Part (aiii) · 1 mark

Give a possible mark for Jais, whose score exceeds 75% of students.

  1. 175% of students scored up to the upper quartile, 86
  2. 2Jais scored more than 86 but no more than the maximum 90, e.g. 88

AnswerAny value V with 86 < V ≤ 90

Part (aiv) · 1 mark

State one comparison between the mark distributions of the two tests.

  1. 1Test 1: median 70; test 2: median 74
  2. 2Test 1: IQR = 86 − 53 = 33; test 2: IQR = 80 − 60 = 20
  3. 3The second test has a higher median, so students did better on the second test

AnswerOne general comment interpreting the median comparison e.g. Students did better on second test OR One general comment interpreting IQR/range comparison e.g. Students marks were more consistent on the 2nd test

Part (b) · 4 marks

Estimate the mean height of the 50 plants from the grouped frequency table.

  1. 1Mid-values: 10, 25, 32, 37, 50
  2. 2Σfx = 4×10 + 9×25 + 20×32 + 15×37 + 2×50 = 40 + 225 + 640 + 555 + 100 = 1560
  3. 3Mean = 1560 ÷ 50 = 31.2 cm

Answer31.2

Part (ci) · 1 mark

Use the histogram and table to find the missing frequency x.

  1. 1Bar for 110 < m ≤ 115 has frequency density 7.6 and width 5
  2. 2x = 7.6 × 5 = 38

Answer38

Part (cii) · 2 marks

Complete the histogram by drawing the missing bars for the remaining mass intervals.

  1. 1115 < m ≤ 125: frequency density = 44 ÷ 10 = 4.4
  2. 2125 < m ≤ 140: frequency density = 51 ÷ 15 = 3.4
  3. 3Draw a bar from 115 to 125 of height 4.4 and a bar from 125 to 140 of height 3.4

AnswerBlocks of heights 4.4 and 3.4 with correct widths

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