Year 11 Eduqas Statistics Case Study Practice | Year 11 Eduqas 统计：案例分析实战演练

📚 Year 11 Eduqas Statistics Case Study Practice | Year 11 Eduqas 统计：案例分析实战演练

In this practical walkthrough, we tackle a realistic statistical investigation from start to finish, mirroring the types of extended case-study questions you will meet in your Year 11 Eduqas GCSE Statistics exam. We collect data on teenagers’ daily social media usage and nightly sleep, then apply a full range of techniques: descriptive statistics, correlation and regression, normal distribution modelling, the chi-squared test for independence and the binomial distribution. Work through each section to deepen your understanding of the statistical enquiry cycle and build confidence for high-mark questions.

在这篇实战演练中，我们将从头到尾完成一个真实的统计调查，模拟你在 Year 11 Eduqas GCSE 统计考试中会遇到的那种长篇案例分析题。我们收集青少年每天使用社交媒体的时长和夜间睡眠时长的数据，然后运用全套技术：描述统计、相关与回归、正态分布建模、卡方独立性检验和二项分布。认真完成每一节，加深你对统计探究循环的理解，为高分题目建立信心。

1. Research Question and Data Collection | 研究问题与数据收集

Our investigation asks: Is there a relationship between the number of hours a teenager spends on social media per day and their average nightly sleep? We also extend the enquiry to examine whether sleep quality differs by gender. The target population is Year 11 students in a large secondary school. A simple random sample of 15 students was selected, and each recorded their typical daily social media use (hours) and average sleep duration (hours) over a week.

我们的调查问题是：青少年每天花在社交媒体上的小时数与夜间平均睡眠时长之间是否存在关系？我们还将探究拓展为：睡眠质量是否因性别而不同。目标总体是一所大型中学的 11 年级学生。我们从中简单随机抽取了 15 名学生，让每人记录一周内每日典型的社交媒体使用时间（小时）和平均睡眠时长（小时）。

The data were collected using a short, anonymous online questionnaire. This method reduces response bias and gives each student an equal chance of being chosen. Ethical considerations, such as informed consent and anonymity, were addressed. The final paired dataset (Social Media hours, Sleep hours) for the 15 students is given below.

数据通过一份简短的匿名在线问卷收集。该方法减少了回答偏差，并让每名学生有平等被抽中的机会。知情同意和匿名等道德考量也已落实。下面给出这 15 名学生的最终配对数据集（社交媒体小时数，睡眠小时数）。

2. Data Presentation and Summary Tables | 数据呈现与汇总表

Before analysis, it is useful to prepare a frequency table for the social media variable after grouping the data. However, for continuous data like sleep duration, a stem-and-leaf diagram often provides a quick picture of the shape and spread. Here we focus on building a grouped frequency distribution for social media hours using class intervals of width 1 hour, from 1 up to 5.

在分析之前，先为社交媒体变量制作一个分组后的频率表很有帮助。不过，对于睡眠时长这样的连续数据，茎叶图往往能快速展现分布形态和分散程度。这里我们重点为社交媒体小时数构建分组频率分布，组距取 1 小时，区间从 1 到 5。

For sleep duration, a stem-and-leaf plot (using stems 6, 7, 8) would show a concentration of values around 6–8 hours, with slight right-skewness. The raw data are sufficient for the detailed statistical calculations that follow.

对于睡眠时长，若使用茎（6, 7, 8）绘制茎叶图，会显示出数据集中在 6–8 小时附近，并略有右偏。原始数据足以支撑接下来的详细统计计算。

3. Descriptive Statistics: Social Media Usage | 描述性统计：社交媒体使用

We first calculate the mean and standard deviation of the social media variable (x). Summing all 15 values gives Σx = 45. The sample mean is therefore x̄ = 45 / 15 = 3.0 hours per day. To measure spread, we compute the sum of squares Σx² = 154.24.

我们先计算社交媒体变量 (x) 的均值和标准差。15 个值求和得 Σx = 45。因此样本均值 x̄ = 45 / 15 = 3.0 小时/天。为度量离散程度，计算平方和 Σx² = 154.24。

Sample variance s²ₓ = (Σx² – (Σx)²/n) / (n – 1) = (154.24 – 45²/15) / 14 = (154.24 – 135) / 14 = 19.24 / 14 ≈ 1.3743. The standard deviation sₓ = √1.3743 ≈ 1.17 hours. The median social media time is the 8th ordered value, which is 3.0 hours (data sorted: 1.0, 1.5, 1.8, 2.0

Published by TutorHao | Year 11 统计 Revision Series | aleveler.com

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