Edexcel Year 13 Statistics: Mock Unit Test Walkthrough | 爱德思Year 13 统计学：单元测试模拟卷精讲

📚 Edexcel Year 13 Statistics: Mock Unit Test Walkthrough | 爱德思Year 13 统计学：单元测试模拟卷精讲

This in-depth article provides a complete walkthrough of a mock unit test designed to mirror the Year 13 Edexcel Statistics syllabus. Covering correlation and regression, conditional probability, the normal distribution, and advanced hypothesis testing (including t-tests), each question is broken down step by step to highlight key techniques, common pitfalls, and essential exam strategies. Use this resource to test your understanding and refine your problem-solving skills before the final assessment.

本文深入解析了一份与Year 13 Edexcel统计学大纲相匹配的模拟单元测试卷。内容涵盖相关与回归、条件概率、正态分布以及高级假设检验（含t检验），对每道题进行逐步拆解，突出重点方法、常见错误和关键考试策略。在最终评估前，借助这份资源检验你的理解并提升解题能力。

1. Introduction and Mock Paper Overview | 模拟卷介绍与概览

This mock unit test is designed for Year 13 students studying Edexcel Statistics (part of the second year of A Level Mathematics). It consists of five compulsory questions worth 10 marks each, totalling 50 marks, and should be completed in roughly 50 minutes. The topics align closely with the statistics component of the Edexcel specification: correlation and regression, conditional probability, normal distribution, t-test for a population mean, and hypothesis testing for the product moment correlation coefficient.

这份模拟单元测试卷面向学习爱德思A Level数学统计模块的Year 13学生。试卷包括5道必答题，每题10分，共50分，建议用时约50分钟。内容紧扣Edexcel大纲的统计学部分：相关与回归、条件概率、正态分布、总体均值的t检验以及积矩相关系数的假设检验。

A formula booklet will be useful, particularly for critical values. Our walkthrough will not only solve each question but also explain the reasoning, intermediate steps, and common exam traps. Remember to show full working—Edexcel awards method marks for correct statistical procedures even if a minor arithmetic slip occurs.

公式手册会非常有用，尤其是查临界值。我们的解析不仅给出每题答案，还会说明推理过程、中间步骤和常见考试陷阱。请记住，Edexcel给分包含过程分，即使出现小的计算失误，正确的统计步骤也能得分。

2. Q1: Correlation and Regression | 问题1：相关与回归

Question 1 presents paired data on hours of revision (x) and test scores (y) for five students. The data table is shown below.

问题1给出了5名学生的复习时间（x）与测试成绩（y）的配对数据。数据如下表所示。

First calculate the means: x̄ = (2+3+5+6+8)/5 = 4.8, and ȳ = (3+4+6+7+10)/5 = 6. Next compute the summary statistics Sxx, Syy and Sxy.

首先计算均值：x̄ = (2+3+5+6+8)/5 = 4.8，ȳ = (3+4+6+7+10)/5 = 6。接着计算汇总统计量Sxx、Syy和Sxy。

Sxx = Σ(x – x̄)² = (2–4.8)² + (3–4.8)² + (5–4.8)² + (6–4.8)² + (8–4.8)² = 7.84 + 3.24 + 0.04 + 1.44 + 10.24 = 22.8

Sxx = Σ(x – x̄)² = 7.84 + 3.24 + 0.04 + 1.44 + 10.24 = 22.8

Syy = Σ(y – ȳ)² = (3–6)² + (4–6)² + (6–6)² + (7–6)² + (10–6)² = 9 + 4 + 0 + 1 + 16 = 30

Syy = 9 + 4 + 0 + 1 + 16 = 30

Sxy = Σ(x – x̄)(y – ȳ) = (–2.8)(–3) + (–1.8)(–2) + (0.2)(0) + (1.2)(1) + (3.2)(4) = 8.4 + 3.6 + 0 + 1.2 + 12.8 = 26

Sxy = 8.4 + 3.6 + 0 + 1.2 + 12.8 = 26

The product moment correlation coefficient is then:

因此，积矩相关系数为：

r = Sxy / √(Sxx × Syy) = 26 / √(22.8 × 30) = 26 / √684 ≈ 26 / 26.153 = 0.994

This value is extremely close to +1, indicating a very strong positive linear correlation. To find the regression line of y on x, we use y – ȳ = b(x – x̄) where b = Sxy / Sxx = 26 / 22.8 ≈ 1.14035. Thus, the equation: y – 6 = 1.140(x – 4.8) → y = 1.14x + 0.528 (approx). Finally, for x = 7 hours, the predicted score is y = 1.140 × 7 + 0.528 = 8.508, roughly 8.5 marks.

该值极为接近+1，表明存在极强的线性正相关。求y对x的回归直线，公式为y – ȳ = b(x – x̄)，其中b = Sxy / Sxx = 26 / 22.8 ≈ 1.14035。方程为y – 6 = 1.140(x – 4.8) → y = 1.14x + 0.528。代入x = 7小时，预测成绩为y = 1.140 × 7 + 0.528 = 8.508，约为8.5分。

3. Q2: Conditional Probability with Replacement | 问题2：放回条件概率

Question 2 sets a scenario: a bag contains 5 red and 3 blue balls. A ball is drawn, the colour is recorded, and it is replaced. Then a second ball is drawn. Draw a tree diagram to represent the outcomes and find the required probabilities.

问题2情景：一个袋子里有5个红球和3个蓝球，随机取一球，记录颜色后放回，再取一球。画出树形图来表示所有结果，并计算指定概率。

The tree diagram has two stages, each with branches labelled ‘Red’ (5/8) and ‘Blue’ (3/8). Since the ball is replaced, the second draw is independent of the first. Four combined outcomes exist: (R,R), (R,B), (B,R), (B,B).

树形图分两层，每层分支标有“Red”（5/8）和“Blue”（3/8）。由于放回，第二次抽取与第一次独立。共有四种组合结果：(R,R)、(R,B)、(B,R)、(B,B)。

Part (b) asks for the probability that both balls are red

Published by TutorHao | Year 13 统计 Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）