📚 KS3 CAIE Statistics: Case Study Practical Exercises | KS3 CAIE 统计：案例分析实战演练
In this article, we will walk through a complete case study covering key KS3 statistics skills, including data collection, organisation, representation, and interpretation. You will see how a real-world question can be explored step by step using fundamental statistical tools.
本文将带您完整演练一个 KS3 统计案例，涵盖数据收集、整理、呈现和解读等核心技能。您将看到如何用基本的统计工具一步步探索一个实际问题。
1. Introducing the Case Study | 案例引入
A secondary school wanted to investigate whether there is any link between daily exercise time and academic performance in mathematics. The PE department and the maths department worked together to collect data from 30 Year 8 students. Each student's daily exercise time (in minutes) and their end-of-year maths score (as a percentage) were recorded. The aim was to see if students who exercise more tend to achieve higher maths scores.
一所中学想要探究每日运动时间与数学学习成绩之间是否存在关联。体育部和数学部合作收集了 30 名 8 年级学生的数据，记录了每位学生每天的运动时间（以分钟计）和他们的年终数学成绩（百分制）。目的是观察运动时间更长的学生是否往往取得更高的数学分数。
The raw data are presented in the table below, with each row representing one student. We will use this dataset throughout our analysis.
原始数据如下表所示，每一行代表一名学生。我们将在整个分析过程中使用这个数据集。
| Student | Exercise (min) | Maths (%) |
|---|---|---|
| 1 | 30 | 65 |
| 2 | 45 | 70 |
| 3 | 50 | 80 |
| 4 | 0 | 55 |
| 5 | 20 | 60 |
| 6 | 60 | 85 |
| 7 | 80 | 90 |
| 8 | 15 | 50 |
| 9 | 0 | 48 |
| 10 | 30 | 72 |
| 11 | 45 | 75 |
| 12 | 55 | 82 |
| 13 | 70 | 88 |
| 14 | 40 | 68 |
| 15 | 35 | 70 |
| 16 | 25 | 62 |
| 17 | 10 | 58 |
| 18 | 60 | 80 |
| 19 | 90 | 92 |
| 20 | 0 | 45 |
| 21 | 35 | 66 |
| 22 | 50 | 78 |
| 23 | 40 | 68 |
| 24 | 30 | 71 |
| 25 | 45 | 73 |
| 26 | 20 | 60 |
| 27 | 15 | 54 |
| 28 | 60 | 82 |
| 29 | 75 | 85 |
| 30 | 30 | 72 |
You can see that the exercise time ranges from 0 minutes (students who did no exercise that day) up to 90 minutes, while maths scores vary between 45% and 92%. This variation will allow us to explore trends and averages.
你可以看到，运动时间从 0 分钟（当天没有运动的学生）到 90 分钟不等，而数学成绩在 45% 到 92% 之间变化。这种差异使我们能够探索趋势和平均值。
2. Data Collection and Types | 数据收集与类型
The data in this case study are primary data because they were collected directly by the school for the specific purpose of this investigation. The exercise variable is continuous quantitative data – it can take any value within a range and was measured to the nearest minute. The maths score is discrete quantitative data in this context, as it is recorded as a whole percentage. Knowing the data type helps us decide which charts and statistics are appropriate.
本案例中的数据是一手数据，因为它们是学校专门为这项调查直接收集的。运动时长这个变量是连续定量数据——它可以在一个范围内取任意值，并且以分钟为单位进行测量。数学成绩在这个情境下是离散定量数据，因为它以整百分比记录。了解数据类型有助于我们选择适当的图表和统计量。
In a well-designed study, it is important to consider whether the sample size is large enough and whether the data collection method is unbiased. Here, 30 students form a reasonable sample
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