A-LevelMathematicsProbability and statistics9709/53 · May/June 2023 · Q48 Marks
The times taken, in minutes, to complete a cycle race by 19 cyclists from each of two clubs, the Cheetahs and the Panthers, are represented in the following back-to-back stem-and-leaf diagram. [Figure 4.1] (Key: 7|9|1 means 97 minutes for Cheetahs and 91 minutes for Panthers)
- (a)Find the median and the interquartile range of the times of the Cheetahs.[3]
- (b)Make two comparisons between the times taken by the Cheetahs and the times taken by the Panthers. The median and interquartile range for the Panthers are 103 minutes and 14 minutes respectively.[2]
- (c)Another cyclist, Kenny, from the Cheetahs also took part in the race. The mean time taken by the 20 cyclists from the Cheetahs was 99 minutes. Find the time taken by Kenny to complete the race.[3]
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 2023). The mark or mark type is shown in brackets.
- [B1] Median = 99 [minutes]
- [M1] [IQR =] 106-83
- [M1] 105 < UQ < 112 – 82 < LQ < 87.
- [A1] 23 [minutes]
- [A1] If M0 scored SC B1 for 23 www.
- [B1] The times for the Cheetahs are faster than the times for the Panthers
- [B1] Correct statement comparing central tendency in context.
- [B1] The times for the Cheetahs are more spread than the times for the Panthers
- [B1] Correct statement comparing range/IQR in context.
- [B1] [Total time including Kenny = 99 × 20 = ]1980
- [B1] Accept unsimplified.
- [M1] For their 1980 – their 1862.
- [A1] = 118 [minutes]
- [A1] Accept 1 hour 58 mins.
- [B1] 1862+ their Kenny's time/20 = 99 seen.
- [M1] For their 99×20 – their 1862.
- [A1] Accept 1 hour 58 mins.
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