O-LevelMathematicsStatistics4024/22 · Oct/Nov 2021 · Q28 Marks
The pie chart summarises the ages of people at a science fair. [Figure showing a pie chart with sectors labeled 'Over 30', 'Under 16', '21 to 30', '16 to 20' and angles 54°, 72°, 144° shown within some sectors, and a right angle symbol]. 250 students entered a science competition. The table summarises their scores. Score (s) | 0 < s ≤ 40 | 40 < s ≤ 60 | 60 < s ≤ 70 | 70 < s ≤ 80 | 80 < s ≤ 100 Frequency | 36 | 48 | 64 | 60 | 42
- (a)(i)Write down the modal class.[1]
- (a)(ii)There were 90 people aged over 30 at the science fair. Calculate the number of people aged 16 to 20.[2]
- (b)(i)Complete the histogram to represent this data. [Figure X.X][3]
- (b)(ii)Students who scored 75 or more are awarded a distinction. Find an estimate for the percentage of the 250 students who were awarded a distinction.[2]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.
- [1]
- [2] M1 for 90/54 [×144] or 144/54 [×90] or 54x = 90 × 144
- [3] B1 for 3 or more rectangles on correct bases B1 for 3 or more correct frequency densities soi
- [2] M1 for (30+42)/250 [×100] oe or for k/250 ×100, where 42 < k < 102 but k ≠ 75
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