题目

Problem

The time taken, $t$ minutes, to complete a puzzle was recorded for each of 150 students. These times are summarised in the table.

Time taken ( $t$ minutes)	$t\leq25$	$t\leq50$	$t\leq75$	$t\leq100$	$t\leq150$	$t\leq200$
Cumulative frequency	16	44	86	104	132	150

(a) Draw a cumulative frequency graph to illustrate the data.

(2)

(b) Use your graph to estimate the 20th percentile of the data.

(1)

题目中文翻译

记录了 150 名学生中每人完成一个谜题所用的时间 $t$ 分钟。这些时间汇总如下表。

所用时间（ $t$ 分钟）	$t\leq25$	$t\leq50$	$t\leq75$	$t\leq100$	$t\leq150$	$t\leq200$
累积频数	16	44	86	104	132	150

(a) 绘制累积频数图来表示这些数据。

(2)

(b) 利用你的图估计这些数据的第 20 百分位数。

(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

展开

表中已经是累计频数，直接在组上界描点，并从原点画平滑递增曲线。

答题过程

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Plot the points

(0,0),\ (25,16),\ (50,44),\ (75,86),

(100,104),\ (150,132),\ (200,150).

Use linear scales, with “Time (minutes)” on the horizontal axis and “Cumulative frequency” on the vertical axis. Join the points with a smooth increasing curve starting at the origin.

(b)

解法一

思路

展开

第20百分位对应累计频数30，在曲线上读横坐标。

答题过程

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The required cumulative frequency is $0.20(150)=30$ . Draw a horizontal line from 30 to the curve, then a vertical line down to the time axis. The estimate is approximately

\boxed{40\text{ minutes}}.

CIE 9709 2022 June Paper 53 Q1

题目

解答

(a)

解法一

思路

答题过程

(b)

解法一

思路

答题过程