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0580/42 May/Jun 2021, Question 4: Estimating the Mean for Grouped Data

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 15 marks

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The question, in short

Using a grouped frequency table for 40 parcel masses, complete a histogram, estimate the mean, find a probability, and work with a box plot for a van's parcels.

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

Part (ai) · 3 marks

Draw the missing histogram bars for the 2 < m ≤ 4, 4 < m ≤ 7 and 7 < m ≤ 12 classes, using frequency density.

  1. 1Frequency density = frequency ÷ class width
  2. 22 < m ≤ 4: 15 ÷ 2 = 7.5; 4 < m ≤ 7: 10 ÷ 3 = 3.33…; 7 < m ≤ 12: 4 ÷ 5 = 0.8
  3. 3Draw bars of these heights across each interval

AnswerCorrect histogram

Part (aii) · 4 marks

Use class midpoints and frequencies to work out an estimated value for the mean parcel mass.

  1. 1Midpoints: 0.75, 1.5, 3, 5.5, 9.5
  2. 2Σfx = 4 × 0.75 + 7 × 1.5 + 15 × 3 + 10 × 5.5 + 4 × 9.5 = 3 + 10.5 + 45 + 55 + 38 = 151.5
  3. 3Mean = 151.5 ÷ 40 = 3.7875 kg

Answer3.7875 or 3.79 or 3.787 or 3.788

Part (aiii) · 1 mark

Work out the chance that a randomly chosen parcel weighs no more than 2 kg.

  1. 1Mass 2 kg or less: 4 + 7 = 11
  2. 2P = 11/40

Answer11/40

Part (aiv) · 3 marks

Choosing two parcels without replacement from those over 2 kg, find the probability of one above 7 kg and one at most 4 kg.

  1. 1Parcels over 2 kg: 15 + 10 + 4 = 29; over 7 kg: 4; 2 to 4 kg: 15
  2. 2P = 4/29 × 15/28 + 15/29 × 4/28
  3. 3= 2 × 60/812 = 120/812 = 30/203

Answer30/203

Part (bi) · 1 mark

Read the middle value from the box-and-whisker plot.

  1. 1Median = 4.6 kg (line inside the box)

Answer4.6

Part (bii) · 1 mark

Work out the spread between the upper and lower quartiles shown on the plot.

  1. 1IQR = 6.2 − 3.0 = 3.2 kg

Answer3.2

Part (biii) · 2 marks

Explain how taking out parcels of 2.4 kg and 5.8 kg changes the median, justifying your conclusion.

  1. 1The median stays the same
  2. 2because one parcel removed (2.4 kg) is below the median and the other (5.8 kg) is above it

AnswerThe median remains the same, and one parcel is below the median and one is above

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Also searched as: 0580/42/M/J/21 · 0580_s21_qp_42 · 0580 s21 42 · question 4.
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