Theory question 105
Data PresentationThe pie chart shows the distribution of marks scored by 200 pupils in a test. (a) How many pupils scored (i) between 41 and 50 marks? (ii) above 60 marks? (b) What fraction of the pupils scored at most 50 marks? (c) What is the modal class?
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Model answer
Angles from the chart: 31–40: 54°, 41–50: 90°, 51–60: 108°, 61–70: 54°, 71–80: 36°, 81–90: 18°.
(a)(i) 90/360 × 200 = 50 pupils.
(ii) Above 60: 54 + 36 + 18 = 108°, so 108/360 × 200 = 60 pupils.
(b) At most 50: 54 + 90 = 144°, so 144/360 = 2/5 of the pupils (80 pupils).
(c) The modal class is 51–60 (largest sector, 108°).
Explanation
Number in a class = angle/360 × total.