Lemmara logoLemmaraWorked solution

0580/43 Oct/Nov 2021, Question 8: Estimating the Mean for Grouped Data

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 15 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Statistics: pie chart for 600 people, a box plot from five summary values, range, mode and median from a dice table, and an estimated mean from grouped times.

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

Part (ai) · 1 mark

Use the 60° tennis sector to show it is 100 people.

  1. 1Tennis = 60/360 × 600 = 100 people

Answer60/360 × 600

Part (aii) · 2 marks

People choosing rugby from a 27° sector.

  1. 1Rugby = 27/360 × 600 = 45 people

Answer45

Part (aiii) · 2 marks

Add cricket (125 people) and swimming to the pie chart.

  1. 1Cricket angle = 125/600 × 360 = 75°
  2. 2Swimming angle = 360 − 105 − 60 − 27 − 75 = 93°
  3. 3Rule a line from the centre to split the remaining space into 75° (cricket) and 93° (swimming)

AnswerCorrect straight line on the pie chart

Part (b) · 3 marks

Draw a box plot from smallest 0.6, range 8.1, median 5.2, LQ 3.4, IQR 4.1.

  1. 1Upper quartile = 3.4 + 4.1 = 7.5; largest = 0.6 + 8.1 = 8.7
  2. 2Draw the box from 3.4 to 7.5 with a line at the median 5.2
  3. 3Draw whiskers from 0.6 to 3.4 and from 7.5 to 8.7

AnswerCorrect diagram: 0.6, 3.4, 5.2, 7.5, 8.7

Part (ci) · 1 mark

Range of the dice scores.

  1. 1Range = 6 − 1 = 5

Answer5

Part (cii) · 1 mark

Modal score.

  1. 1Highest frequency is 25, so mode = 2

Answer2

Part (ciii) · 1 mark

Median of 100 rolls.

  1. 1Median is between the 50th and 51st scores
  2. 2Cumulative frequencies: 16, 41, 58, so both are 3
  3. 3Median = 3

Answer3

Part (d) · 4 marks

Estimate the mean time from five class intervals using midpoints.

  1. 1Mid-values: 15, 22.5, 27.5, 40, 65
  2. 2Σfx = 2×15 + 8×22.5 + 12×27.5 + 16×40 + 12×65
  3. 3= 30 + 180 + 330 + 640 + 780 = 1960
  4. 4Mean = 1960 ÷ 50 = 39.2 seconds

Answer39.2

Stuck on a step? Read the free lesson: Estimating the Mean for Grouped Data

Practise more estimating the mean for grouped data questions

Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on estimating the mean for grouped data

Also searched as: 0580/43/O/N/21 · 0580_w21_qp_43 · 0580 w21 43 · question 8.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.