0580/41 Oct/Nov 2021, Question 3: Box-and-whisker plot

Part (a) · 4 marks

Draw a box-and-whisker plot on the grid using the cumulative frequency diagram.

1. 1Min = 30, max = 90
2. 2Median: cf 40 gives 63; LQ: cf 20 gives 50; UQ: cf 60 gives 72
3. 3Draw the box from 50 to 72 with a line at 63, whiskers to 30 and 90

AnswerCorrect box-and-whisker plot

Part (bi) · 2 marks

Estimate the 30th percentile mass from the cumulative frequency diagram.

1. 130% of 80 = 24
2. 2Cf 24 gives mass = 56 kg

Answer56

Part (bii) · 2 marks

Estimate how many boys weigh more than 75 kg using the diagram.

1. 1At 75 kg, cf = 64
2. 280 − 64 = 16

Answer16

Part (ci) · 1 mark

Complete the missing frequency in the table using the cumulative frequency diagram.

1. 1Cf at 50 = 20, at 60 = 34, at 70 = 56
2. 250−60: 34 − 20 = 14; 60−70: 56 − 34 = 22

Answer14, 22

Part (cii) · 4 marks

Estimate the mean mass from the given frequency table.

1. 1Midpoints 35, 45, 55, 65, 75, 85
2. 2Σfx = 35×8 + 45×12 + 55×14 + 65×22 + 75×14 + 85×10
3. 3= 280 + 540 + 770 + 1430 + 1050 + 850 = 4920
4. 4Mean = 4920 ÷ 80 = 61.5 kg

Answer61.5

Part (ciii) · 3 marks

For two boys picked at random from those over 70 kg, find the probability that one is over 80 kg and the other is 80 kg or less.

1. 1Over 70 kg: 24 boys, 10 over 80 kg and 14 not
2. 2P = 10/24 × 14/23 + 14/24 × 10/23
3. 3= 2 × 140/552 = 280/552 = 35/69

Answer35/69

More past-paper questions on box-and-whisker plot

• 0580/42 Feb/Mar 2023 Q2 · 15 marks
• 0580/41 May/Jun 2021 Q8 · 10 marks