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CIE 9709 2024 June Paper 53 Q4

A Level / CIE / S1

CIE 9709 2024 June Paper 53 Paper · Question 4

题目

Problem

The times taken, in seconds, by 15 members of each of two swimming clubs, the Penguins and the Dolphins, to swim 50 metres are shown in the following table.

Penguins353942444545485056585961666872
Dolphins364143484949505154565660616471

(a) Draw a back-to-back stem-and-leaf diagram to represent this information, with Penguins on the left-hand side.

(4)

The diagram shows a box-and-whisker plot representing the times for the Penguins.

(b) On the same diagram, draw a box-and-whisker plot to represent the times for the Dolphins.

(3)

(c) Hence state one difference between the distributions of the times for the Penguins and the Dolphins.

(1)
题目中文翻译

Penguins 和 Dolphins 两个游泳俱乐部各有 15 名会员,其游完 50 米所用的时间(以秒为单位)如下表所示。

Penguins353942444545485056585961666872
Dolphins364143484949505154565660616471

(a) 画一幅背靠背茎叶图表示这些数据,并将 Penguins 的数据画在左侧。

(4)

图中给出了表示 Penguins 所用时间的箱线图。

(b) 在同一幅图中画出表示 Dolphins 所用时间的箱线图。

(3)

(c) 由此指出 Penguins 与 Dolphins 所用时间的分布之间的一个差异。

(1)
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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以十位为茎、个位为叶,左侧Penguins从茎向外递增,图例同时解释两侧及秒单位。

答题过程

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Use stems 3,4,5,6,73,4,5,6,7, with Penguins on the left and Dolphins on the right. Order leaves away from the stem on both sides.

Key: 2∣4∣12\mid4\mid1 means 42 seconds for Penguins and 41 seconds for Dolphins.

(b)

解法一

思路

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15个数据的中位数为第8个,四分位数为第4、第12个。给定Penguins箱线图保留,在同一刻度补Dolphins。

答题过程

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For Dolphins, the five-number summary is

minimum=36,Q1=48,median=51,\text{minimum}=36,\quad Q_1=48,\quad \text{median}=51, Q3=60,maximum=71(seconds).Q_3=60,\quad \text{maximum}=71 \qquad\text{(seconds)}.

On the same time scale as the Penguins plot, draw a box from 48 to 60 with a median line at 51. Draw whiskers to 36 and 71, and label it “Dolphins”.

(c)

解法一

思路

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由(b)比较四分位距,用具体数值支持一致性结论,只给题目要求的一个差异。

答题过程

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The Dolphins have more consistent swimming times: their interquartile range is 60−48=1260-48=12 seconds, compared with 61−44=1761-44=17 seconds for the Penguins.