Ransha measured the lengths, in centimetres, of 160 palm leaves. His results are illustrated in the cumulative frequency graph below. [Figure with cumulative frequency graph]
- (i)Estimate how many leaves have a length between 14 and 24 centimetres.[1]
- (ii)10% of the leaves have a length of L centimetres or more. Estimate the value of L.[2]
- (iii)Estimate the median and the interquartile range of the lengths.[3]
- (iv)Sharim measured the lengths, in centimetres, of 160 palm leaves of a different type. He drew a box-and-whisker plot for the data, as shown on the grid below. Compare the central tendency and the spread of the two sets of data.[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 2019). The mark or mark type is shown in brackets.
- [B1] 98 ≤ answer < 100
- [M1] 144 seen, may be marked on graph
- [A1] (L =) 22
- [B1] 15.5 < median < 15.8
- [M1] 18.5 < UQ < 19 – 12.5 < LQ < 13
- [A1] 6.0 ≤ IQR < 6.2
- [B1] Any correct comparison of central tendency, must mention median
- [B1] Any correct comparison of spread, must refer to IQR
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