题目
Last Saturday, a cycling competition for teams of 11 cyclists took place. For each cyclist, the time taken to complete the course was recorded to the nearest minute. The times taken by the cyclists from two teams, the Linnets and the Puffins, are shown in the following table.
| Linnets | 48 | 51 | 54 | 57 | 59 | 60 | 64 | 64 | 65 | 68 | 70 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Puffins | 45 | 49 | 51 | 55 | 55 | 58 | 59 | 62 | 64 | 64 | 74 |
(a) Draw a back-to-back stem-and-leaf diagram to represent this information, with Linnets on the left-hand side.
(b) Find the interquartile range of the times taken by the Linnets.
(c) On the grid below, draw a box-and-whisker plot to represent the information for the Linnets and the Puffins.
(d) Make one comparison between the times taken by the Linnets and the times taken by the Puffins.
题目中文翻译
上周六举行了一场自行车团体赛，每队有 11 名骑手。记录了每名骑手完成赛程所用的时间，并取至最接近的分钟数。Linnets 和 Puffins 两队骑手的用时如下表所示。
| Linnets | 48 | 51 | 54 | 57 | 59 | 60 | 64 | 64 | 65 | 68 | 70 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Puffins | 45 | 49 | 51 | 55 | 55 | 58 | 59 | 62 | 64 | 64 | 74 |
(a) 画出背靠背茎叶图表示这些数据，将 Linnets 队的数据放在左侧。
(b) 求 Linnets 队用时的四分位距。
(c) 在下方网格上画出箱线图，表示 Linnets 和 Puffins 两队的数据。
(d) 对 Linnets 队与 Puffins 队的用时作出一项比较。
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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十位为茎、个位为叶，Linnets放在左侧，并由茎向外递增。重复值都需要保留，图例同时注明队名与分钟单位。
答题过程
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Use tens as stems and units as leaves, with Linnets on the left.
Key: means 54 minutes for Linnets and 55 minutes for Puffins.
(b)
解法一
思路
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11个已排好序的数据，中位数为第6个，去掉后两侧各5个数据。下、上四分位数分别为原数据第3与第9个值。
答题过程
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For Linnets, the lower quartile is the 3rd value, 54 minutes, and the upper quartile is the 9th value, 65 minutes. Hence
(c)
解法一
思路
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分别求两队五数概括，使用同一时间刻度画箱线图。须线从箱体中部伸到最小值、最大值，并标清队名。
答题过程
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The five-number summaries are:
| Team | Minimum | Lower quartile | Median | Upper quartile | Maximum |
|---|---|---|---|---|---|
| Linnets | |||||
| Puffins |
Draw the two box-and-whisker plots using a common linear scale labelled “Time (minutes)”, and label each team.
(d)
解法一
思路
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比较须放在骑行所需时间的情境中，而不是只罗列中位数。Puffins中位时间较短，表示典型完成时间更快。
答题过程
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The Puffins were faster on average, as their median time was 58 minutes compared with 60 minutes for the Linnets.