GCSE Edexcel Statistics: Case Study Practical Walkthrough | GCSE Edexcel 统计：案例分析实战演练

📚 GCSE Edexcel Statistics: Case Study Practical Walkthrough | GCSE Edexcel 统计：案例分析实战演练

This article walks you through a complete GCSE Edexcel Statistics case study, from formulating a hypothesis to drawing conclusions. You will see how real data on students’ social media usage and maths scores can be analysed using descriptive statistics, correlation, regression, probability and hypothesis testing. Follow each step closely to build the skills needed for your exam.

本文将带你完整演练一个 GCSE Edexcel 统计案例，从提出假设到得出结论。你将看到如何利用描述统计、相关性、回归、概率和假设检验来分析学生社交媒体使用时间与数学成绩的真实数据。仔细跟随每一步，扎实掌握考试所需的实践技能。

1. Understanding the Investigation & Forming Hypotheses | 理解调查与形成假设

A school wants to investigate whether there is a relationship between the time students spend on social media each day and their performance in a recent mathematics test. The research question is: ‘Is more time on social media associated with lower maths scores?’ Before collecting data, we define a null hypothesis (H₀) that there is no correlation in the population, and an alternative hypothesis (H₁) that a negative correlation exists. We also set up a separate claim to test: ‘More than 50% of students use social media for over 3 hours a day.’ This will be examined later with a binomial test.

某学校想研究学生每天花在社交媒体上的时间与其近期数学测验成绩之间是否存在关联。研究问题是：“社交媒体使用时间越长，数学成绩是否越低？”在收集数据之前，我们定义原假设（H₀）为总体中不存在相关性，备择假设（H₁）为存在负相关。此外，我们还设定了另一个待检验的声称：“超过 50% 的学生每天使用社交媒体超过 3 小时。”这将在后续用二项检验进行分析。

To keep the investigation focused, we choose a target population of Year 11 students in one school and decide to use a sample of 20 students. The variables are the daily social media time in hours (to the nearest 0.1 hour) and the maths test score out of 50. Both are continuous numerical variables, making a scatter graph and Pearson’s correlation coefficient appropriate.

为了让研究聚焦，我们选择某学校11年级学生作为目标总体，并决定抽取20名学生作为样本。变量为每天社交媒体使用时间（以小时计，精确到 0.1 小时）和数学测验分数（满分 50 分）。两者均为连续数值变量，因此散点图和皮尔逊相关系数方法是合适的。

2. Data Collection and Sampling | 数据收集与抽样

A simple random sample of 20 students was drawn from the Year 11 register using a random number generator. Each selected student was asked to record their screen time for social media apps over one week, and the daily average was calculated. Their latest maths test score was obtained from school records with consent. This is primary data because it was collected specifically for the investigation, and the sampling method helps reduce bias.

使用随机数生成器从11年级学生名册中抽取了20名简单随机样本。被选中的学生记录一周内社交应用屏幕使用时间，计算每日平均值。在获得同意后，从学校记录中获取他们最近一次数学测验成绩。由于数据专为本次调查收集，这属于一手数据，且该抽样方法有助于降低偏差。

In reality, exam questions often describe the sampling method and ask you to critique it. For example, a random sample might still suffer from non‑response if some students refuse to share their screen time. Also, screen time data may be inaccurate if students forget to track it properly. These limitations will be discussed in the evaluation later.

实际考题中往往会描述抽样方法并要求你进行批判。例如，简单随机样本可能仍存在无回答偏差，如果有学生拒绝分享屏幕使用时间。此外，如果学生忘记正确记录，屏幕时间数据也可能不准确。这些局限性将在后续评估中讨论。

3. Data Presentation and Tables | 数据展示与表格

The table below shows the data for the first six students. The full dataset of 20 students is used for all calculations that follow.

下表显示了前六名学生的数据。随后的所有计算均使用完整的 20 名学生数据集。

Organising raw data in a clear table allows you to spot patterns quickly. Notice that as social media time increases, the maths score tends to decrease – a hint of a negative association. Before drawing conclusions, however, we need to compute summary statistics and a measure of correlation.

将原始数据整理成清晰的表格能让你快速发现规律。请注意，随着社交媒体使用时间增加，数学成绩呈下降趋势——这暗示存在负向关联。然而，在得出结论之前，我们需要计算汇总统计量和相关性度量。

4. Measures of Central Tendency | 集中趋势度量

For the social media time, the sample mean x̄ is calculated by summing all 20 values (57.9 hours) and dividing by 20. This gives x̄ = 2.90 hours (to 2 d.p.). The median is the average of the 10th and 11th ordered values; after sorting the data, the median equals 2.75 hours. Because the mean and median are close, the distribution is roughly symmetric, though slightly skewed right by a few high values like 6.0 hours.

对于社交媒体使用时间，样本均值 x̄ 通过将所有20个数值求和（57.9 小时）再除以 20 得到，结果为 x̄ = 2.90 小时（保留两位小数）。中位数为排序后第10和第11个值的平均数，计算得出中位数为 2.75 小时。由于均值与中位数接近，分布大致对称，但因存在如 6.0 小时这样的高值而轻微右偏。

For maths scores, the sum of all 20 scores is 663, so the mean ȳ = 33.15. The ordered data give a median of 32.5. Again, the two averages are similar, suggesting a fairly balanced spread of scores around the centre. When comparing groups, the mean is useful, but the median is more robust if outliers are present.

数学成绩方面，20 个分数总和为 663，因此均值 ȳ = 33.15。排序后得到的中位数为 32.5

Published by TutorHao | GCSE 统计 Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）