📚 Case Study Practice in Statistics | 统计案例分析实战演练
Statistics comes alive when you explore real data. This article walks through a complete case study, from designing a survey to drawing conclusions. You will practise planning, collecting, organising and interpreting data, just as required in the OCR Year 9 statistics curriculum.
当你探索真实数据时，统计学才真正生动起来。本文将带你走完一个完整的案例研究，从设计调查问卷到得出结论。你将练习规划、收集、整理和解释数据，完全贴合 OCR 九年级统计课程的要求。
1. Setting the Scene | 案例背景设定
A school wants to know how Year 9 students spend their free time and whether screen time affects their sleep. The school council decides to carry out a statistical investigation. Your job is to plan and execute this study using sound statistical methods.
一所学校想了解九年级学生如何度过课余时间，以及屏幕时间是否影响睡眠。学生会决定开展一项统计调查。你的任务是用可靠的统计方法规划和执行这项研究。
2. Defining the Research Question | 明确研究问题
A focused question drives the whole investigation. We phrase it as: 'Is there a relationship between daily screen time and hours of sleep among Year 9 students?' A clear question helps us decide what data to collect and how to analyse it.
一个聚焦的问题推动整个调查。我们将问题表述为：“九年级学生的每日屏幕时间与睡眠时长之间是否存在关系？”清晰的问题有助于我们决定收集哪些数据以及如何分析。
3. Planning the Data Collection | 数据收集计划
We choose a questionnaire because it can gather information from many pupils quickly. The questionnaire will ask about: age, gender, daily screen time (in hours), hours of sleep per night, and main free‑time activity. All responses will be anonymous to encourage honesty.
我们选择问卷调查，因为它可以快速从许多学生那里收集信息。问卷将询问：年龄、性别、每日屏幕时间（小时）、每晚睡眠时长及主要课余活动。所有回答均匿名，以鼓励诚实作答。
4. Sampling Method | 抽样方法
It is impractical to survey all 180 Year 9 students, so we take a stratified sample. We divide the year group into tutor groups and randomly select 10 students from each. This ensures fair representation across different classes.
调查所有 180 名九年级学生不太现实，因此我们采用分层抽样。按辅导班分层，从每个班随机抽取 10 名学生。这确保了不同班级的公平代表性。
5. Collecting the Raw Data | 收集原始数据
Thirty questionnaires are returned. Here are the first few rows of our data table:
回收了 30 份问卷。以下是我们数据表的前几行：
| Pupil | Screen (h) | Sleep (h) | Activity |
|---|---|---|---|
| A | 5.5 | 7.0 | Gaming |
| B | 3.0 | 8.5 | Reading |
| C | 7.0 | 6.5 | Social media |
We record screen time to the nearest half hour and sleep to the nearest 0.5 hour.
我们以半小时为精度记录屏幕时间，睡眠时长精确到 0.5 小时。
6. Organising and Cleaning Data | 数据整理与清洗
We spot one pupil reported 15 h of screen time; this is checked and found to be a misunderstanding—they meant 1.5 h. The value is corrected. We also group screen time into intervals for a frequency table: 0–2, 2–4, 4–6, 6–8, 8–10 hours.
我们发现一名学生报告了 15 小时屏幕时间；经核实是误解——他们本意是 1.5 小时。我们修正了该值。接着将屏幕时间分组以制作频数表：0–2、2–4、4–6、6–8、8–10 小时。
7. Displaying Data with Charts | 用图表展示数据
We draw a dual bar chart comparing average sleep for 'low screen' (less than 4 h) and 'high screen' (4 h or more) pupils. The 'low screen' group averages 8.3 h sleep, while the 'high screen' group averages 6.9 h. The chart makes the difference clear at a glance.
我们绘制了一个对比“低屏幕”（少于 4 小时）和“高屏幕”（4 小时及以上）学生平均睡眠的双条形图。“低屏幕”组平均睡眠 8.3 小时，“高屏幕”组平均睡眠 6.9 小时。图表让差异一目了然。
8. Calculating Averages and Spread | 计算平均数与离散程度
For all 30 pupils, the mean screen time is 4.7 h and the mean sleep is 7.4 h. The median screen time is 4.5 h, close to the mean. The range of sleep is from 5.5 h to 9.5 h, giving a spread of 4.0 h, which shows considerable variation in sleep habits.
全部 30 名学生的屏幕时间均值为 4.7 小时，睡眠均值 7.4 小时。屏幕时间中位数 4.5 小时，与均值接近。睡眠的极差从 5.5 小时到 9.5 小时，跨度为 4.0 小时，表明睡眠习惯差异较大。
9. Drawing a Scatter Graph | 绘制散点图
We plot screen time on the x-axis and sleep on the y-axis for each pupil. The points show a general downward trend: as screen time increases, sleep tends to decrease. We describe the correlation as moderately negative.
我们以散点图绘制每位学生的屏幕时间（x 轴）与睡眠时长（y 轴）。数据点呈现整体下降趋势：屏幕时间越长，睡眠往往越少。我们将相关性描述为中等负相关。
10. Looking for Patterns and Outliers | 寻找规律与异常值
Most pupils with screen time above 6 h sleep less than 7 h. One pupil with 1 h screen time only sleeps 6 h; this outlier could be due to other factors like homework or part‑time job. Outliers remind us that correlation does not imply causation.
大多数屏幕时间超过 6 小时的学生睡眠不足 7 小时。一名屏幕时间仅 1 小时的学生只睡 6 小时；这个异常值可能缘于作业或打工等其他因素。异常值提醒我们，相关性不代表因果性。
11. Drawing Conclusions | 得出结论
Our evidence suggests a negative association: higher screen time is linked to shorter sleep. However, the relationship is not strict, and other variables such as sport or study time also play a role. We recommend further research with a larger sample and more detailed questions.
我们的证据表明存在负相关：高屏幕时间与较短睡眠相关。然而，这种关系并非严格，运动或学习时间等其他变量也在起作用。我们建议用更大样本和更详细问题做进一步研究。
12. Evaluating the Study | 评估研究
The questionnaire was quick and cheap but relied on self‑reported data, which may not be perfectly accurate. The sample size of 30 is fairly small, so results might not represent all Year 9 students. In future, we could use apps to track screen time objectively and include more students.
问卷快捷且成本低，但依赖自我报告数据，可能不够精确。样本量 30 偏小，结果或许不能代表所有九年级学生。将来我们可以用应用程序客观追踪屏幕时间，并纳入更多学生。
Published by TutorHao | Statistics Revision Series | aleveler.com
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