Year 12 Edexcel Statistics: Mock Unit Test Walkthrough | 爱德思 Year 12 统计：单元测试模拟卷解析

📚 Year 12 Edexcel Statistics: Mock Unit Test Walkthrough | 爱德思 Year 12 统计：单元测试模拟卷解析

This mock unit test is designed for Year 12 students following the Edexcel Statistics specification. It covers key topics from data collection to hypothesis testing, providing a realistic exam-style experience. Work through each question carefully and review the detailed solutions to consolidate your understanding.

本模拟单元测试专为学习爱德思统计课程的 Year 12 学生设计。它涵盖了从数据收集到假设检验的关键主题，提供真实的考试风格体验。请仔细解答每一道题，并通过详细的解析来巩固你的理解。

1. About This Mock Test | 模拟卷简介

The paper consists of 7 questions worth a total of 50 marks, and you should spend about 50 minutes on it. Topics include measures of location and spread, data representations, probability, correlation and regression, binomial and normal distributions, and hypothesis testing. Each question is followed by a step-by-step bilingual solution to help you identify common pitfalls and reinforce key concepts.

本试卷包含 7 道题，满分 50 分，建议用时约 50 分钟。覆盖的内容包括位置与分散度量、数据表示、概率、相关与回归、二项分布与正态分布，以及假设检验。每道题后配有逐步的中英双语解析，帮助你识别常见错误并巩固核心概念。

2. Question 1 – Mean and Standard Deviation | 第1题 – 均值与标准差

A biologist measures the lengths (in cm) of 10 leaves: 10, 12, 15, 18, 20, 11, 14, 16, 19, 17. Calculate the sample mean and the sample standard deviation, showing all your working.

一位生物学家测量了 10 片叶子的长度（单位：cm）：10, 12, 15, 18, 20, 11, 14, 16, 19, 17。请计算样本均值和样本标准差，并写出全部计算过程。

First, compute the sum of the data: Σx = 10 + 12 + 15 + 18 + 20 + 11 + 14 + 16 + 19 + 17 = 152.

首先计算数据的总和：Σx = 10 + 12 + 15 + 18 + 20 + 11 + 14 + 16 + 19 + 17 = 152。

The sample mean is x̄ = Σx / n = 152 / 10 = 15.2 cm.

样本均值为 x̄ = Σx / n = 152 / 10 = 15.2 cm。

Next, find Σx² = 10² + 12² + 15² + 18² + 20² + 11² + 14² + 16² + 19² + 17² = 100 + 144 + 225 + 324 + 400 + 121 + 196 + 256 + 361 + 289 = 2416.

接下来计算 Σx² = 10² + 12² + 15² + 18² + 20² + 11² + 14² + 16² + 19² + 17² = 100 + 144 + 225 + 324 + 400 + 121 + 196 + 256 + 361 + 289 = 2416。

For a sample, the sum of squares about the mean is Sxx = Σx² − (Σx)² / n = 2416 − (152)² / 10 = 2416 − 2310.4 = 105.6.

对于样本，离均差平方和为 Sxx = Σx² − (Σx)² / n = 2416 − (152)² / 10 = 2416 − 2310.4 = 105.6。

The sample variance is s² = Sxx / (n − 1) = 105.6 / 9 ≈ 11.7333 cm².

样本方差为 s² = Sxx / (n − 1) = 105.6 / 9 ≈ 11.7333 cm²。

Therefore, the sample standard deviation is s = √(11.7333) ≈ 3.43 cm (to 3 significant figures).

因此，样本标准差为 s = √(11.7333) ≈ 3.43 cm（保留三位有效数字）。

3. Question 2 – Box Plots and Outliers | 第2题 – 箱线图与异常值

The waiting times (in minutes) at a bus stop are recorded: 22, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 55. Construct a box plot and identify any outliers.

某公交车站的等候时间（分钟）记录如下：22, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 55。请绘制箱线图并识别任何异常值。

There are 12 data values. First, order the data from smallest to largest. The minimum is 22, the maximum is 55.

共有 12 个数据。首先将数据从小到大排序。最小值为 22，最大值为 55。

To find the quartiles: Q1 is the median of the lower half. For n = 12, the position is (12 + 1) / 4 = 3.25, so Q1 lies between the 3rd value (26) and the 4th (28). Using interpolation: Q1 = 26 + 0.25 × (28 − 26) = 26.5 minutes.

求四分位数：Q1 是下半部分的中位数。n = 12 时，位置为 (12 + 1) / 4 = 3.25，因此 Q1 位于第 3 个值（26）和第 4 个值（28）之间。使用插值：Q1 = 26 + 0.25 × (28 − 26) = 26.5 分钟。

The median (Q2) position is (12 + 1) / 2 = 6.5, between the 6th (30) and 7th (31): Q2 = 30 + 0.

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

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