CAIE Year 12 Statistics Unit Test Mock Paper Walkthrough | CAIE 12年级统计单元测试模拟卷解析

📚 CAIE Year 12 Statistics Unit Test Mock Paper Walkthrough | CAIE 12年级统计单元测试模拟卷解析

This walkthrough covers a full CAIE AS-Level Statistics mock paper, tackling data representation, measures of location and spread, probability, discrete random variables, and the normal distribution. Each section presents a question in the mock paper followed by step-by-step solutions, helping you master key S1 concepts.

本文完整解析一套CAIE统计AS模拟卷，涵盖数据表示、集中趋势与离散程度、概率、离散随机变量和正态分布。每个小节给出模拟题及分步解答，助你掌握S1核心要点。

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1. Stem-and-Leaf Diagram & Quartiles | 茎叶图与四分位数

Question: The marks of 15 students in a test are: 34, 42, 45, 48, 33, 39, 51, 55, 56, 60, 29, 31, 40, 52, 47.Give an ordered stem-and-leaf diagram and find the median and interquartile range. [6 marks]

题目：15名学生的测验成绩为：34,42,45,48,33,39,51,55,56,60,29,31,40,52,47。绘制有序茎叶图，并求中位数与四分位距。[6分]

First, arrange the data in ascending order: 29, 31, 33, 34, 39, 40, 42, 45, 47, 48, 51, 52, 55, 56, 60.

首先将数据升序排列：29, 31, 33, 34, 39, 40, 42, 45, 47, 48, 51, 52, 55, 56, 60。

Stem-and-leaf: 2 | 9 ; 3 | 1 3 4 9 ; 4 | 0 2 5 7 8 ; 5 | 1 2 5 6 ; 6 | 0. Use key 2|9 = 29.

茎叶图：2 | 9 ; 3 | 1 3 4 9 ; 4 | 0 2 5 7 8 ; 5 | 1 2 5 6 ; 6 | 0。 图例 2|9 表示 29。

Median position: (15+1)/2 = 8th value, so median = 45.

中位数位置：(15+1)/2 = 第8位，中位数 = 45。

Lower half (first 7 values): 29,31,33,34,39,40,42 → Q₁ is the 4th value = 34.

下半组（前7个值）：29,31,33,34,39,40,42 → 下四分位数 Q₁ 为第4位 = 34。

Upper half (last 7 values): 47,48,51,52,55,56,60 → Q₃ is the 4th value = 52.

上半组（后7个值）：47,48,51,52,55,56,60 → 上四分位数 Q₃ 为第4位 = 52。

IQR = Q₃ − Q₁ = 52 − 34 = 18.

四分位距 IQR = Q₃ − Q₁ = 52 − 34 = 18。

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2. Box Plots and Outliers | 箱线图与离群值

Continue with Question 1(c): Using the same data, construct a box plot and check for outliers using the 1.5 × IQR rule. [4 marks]

继续题1(c)：用同一组数据绘制箱线图，并用1.5×IQR准则检查离群值。[4分]

Five-number summary: minimum = 29, Q₁ = 34, median = 45, Q₃ = 52, maximum = 60.

五数综合法：最小值=29，Q₁=34，中位数=45，Q₃=52，最大值=60。

Lower fence = Q₁ − 1.5 × IQR = 34 − 1.5×18 = 34 − 27 = 7.

下界限 = 34 − 1.5×18 = 7。

Upper fence = Q₃ + 1.5 × IQR = 52 + 27 = 79.

上界限 = 52 + 27 = 79。

Since all data values lie between 7 and 79, there are no outliers. The box plot has whiskers extending from 29 to 60.

所有数据均在7至79之间，故无离群值。箱线图的触须从29延伸到60。

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3. Histogram & Frequency Density | 直方图与频率密度

Question 2(a): A survey recorded the time (minutes) students spent on a task: 0–5 (10 students), 5–15 (25), 15–30 (30), 30–40 (5). Draw the histogram with frequency density on the vertical axis. [5 marks]

题目2(a)：一项调查记录学生完成任务的时间（分钟）：0–5 (10人), 5–15 (25人), 15–30 (30人), 30–40 (5人)。绘制频率密度为纵轴的直方图。[5分]

Calculate class widths: 0–5 has width 5, 5–15 width 10, 15–30 width 15, 30–40 width 10.

计算组距：0–5组距5, 5–15组距10, 15–30组距15, 30–40组距10。

Frequency density = frequency ÷ class width. The densities are: 10÷5 = 2, 25÷10 = 2.5, 30÷15 = 2, 5÷10 = 0.5.

频率密度 = 频率 ÷ 组距。各分组密度为：2, 2.5, 2, 0.5。

The histogram bars should be drawn with widths matching the class intervals and heights representing the frequency densities.

直方图的条宽对应组距，条高对应频率密度。

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4. Estimating Mean & Standard Deviation | 估算均值与标准差

Question 2(b): Using midpoints, estimate the mean and standard deviation of the time spent. [6 marks]

题2(b)：利用组中值估算时间的均值和标准差。[6分]

Midpoints: 2.5, 10,

Published by TutorHao | Year 12 统计 Revision Series | aleveler.com

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