O-LevelMathematicsStatistics4024/22 · May/June 2024 · Q913 Marks
A shop sells two varieties of apple tree.
- (a)(i)(a)The cumulative frequency diagram shows the heights, in metres, of 80 Variety A trees. [Figure 9.1] Use the diagram to estimate the median[1]
- (a)(i)(b)the 30th percentile.[2]
- (a)(ii)Trees with a height greater than y m are graded Class I. 2/5 of the 80 trees are graded Class I. Find the value of y.[2]
- (a)(iii)Complete the frequency table for the heights of the Variety A trees. Height (h m) 1.1 < h <= 1.2 1.2 < h <= 1.3 1.3 < h <= 1.4 1.4 < h <= 1.5 1.5 < h <= 1.6 Frequency 6 24[2]
- (b)The frequency table shows the heights of 50 Variety B trees. Height (h m) 1.5 < h <= 1.7 1.7 < h <= 1.8 1.8 < h <= 1.9 1.9 < h <= 2.3 Frequency p 15 17 q Using the midpoints of the intervals, the estimated mean height of these Variety B trees is 1.81 m. Calculate the value of p and the value of q.[6]
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 (May/June 2024). The mark or mark type is shown in brackets.
- [1] 1.33 to 1.335
- [2] 1.28 to 1.285
- M1 for 30/100 × 80 oe
- [2] 1.355 to 1.36
- B1 for 48 soi
- [2] 28 18 4
- B1 for one correct
- [6] p = 10 / q = 8
- B5 for 1.6p + 2.1q = 32.8 oe soi and p + q + 15 + 17 = 50 oe
- or 0.21p -0.29q = -0.22 oe soi and p + q + 15 + 17 = 50 oe
- OR
- B4 for 1.6p + 2.1q = 32.8 oe soi
- or 0.21p -0.29q = -0.22 oe soi
- OR
- B1 for p + q + 15 + 17 = 50 oe
- B1 for correct midpoints soi
- M2 for (1.6×p+1.75×15+1.85×17+2.1×q) / 50 =1.81 oe soi
- or (1.6×p+1.75×15+1.85×17+2.1×q) / (p+q+15+17) =1.81 oe soi
- or M1 for (1.6×p+1.75×15+1.85×17+2.1×q) / 50 soi
- or (1.6×p+1.75×15+1.85×17+2.1×q) / (p+q+15+17) soi
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