题目
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.
(a) Find the median and the interquartile range of the times of the Cheetahs.
The median and interquartile range for the Panthers are 103 minutes and 14 minutes respectively.
(b) Make two comparisons between the times taken by the Cheetahs and the times taken by the Panthers.
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.
(c) Find the time taken by Kenny to complete the race.
题目中文翻译
Cheetahs 和 Panthers 两家俱乐部各有 19 名自行车运动员完成一场自行车比赛，他们所需的时间（单位为分钟）用下面的背靠背茎叶图表示。
(a) 求 Cheetahs 运动员用时的中位数和四分位距。
Panthers 运动员用时的中位数和四分位距分别为 103 分钟和 14 分钟。
(b) 就 Cheetahs 与 Panthers 运动员的用时作出两项比较。
Cheetahs 的另一名自行车运动员 Kenny 也参加了比赛。Cheetahs 的这 20 名自行车运动员用时的均值为 99 分钟。
(c) 求 Kenny 完成比赛所需的时间。
原卷通用作答要求
Answer all questions. You should use a calculator where appropriate.
You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.
请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。
解答
(a)
解法一
思路
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19个数据的中位数为第10项，四分位数为第5与第15项。
答题过程
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For the Cheetahs, the 10th ordered time is 99 minutes, so the median is 99 minutes.
The 5th and 15th times are 83 and 106 minutes. Hence
(b)
解法一
思路
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分别比较中央趋势及离散程度，解释用时较少就是较快。
答题过程
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The Cheetahs are typically faster, because their median time is 99 minutes, below the Panthers’ 103 minutes.
The Cheetahs’ times are less consistent, because their interquartile range is 23 minutes, above the Panthers’ 14 minutes.
(c)
解法一
思路
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从图中加总原19人时间，再用20人的总时间减去该总和。
答题过程
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The 19 Cheetahs’ times, in increasing order, are
Their total is 1862 minutes. The total for all 20 cyclists including Kenny is minutes. Therefore Kenny’s time is