📚 Year 9 CAIE Statistics: Case Study Practical Exercises | Year 9 CAIE 统计：案例分析实战演练
This article walks you through a complete statistical investigation suitable for Year 9 CAIE Statistics. You will follow a student who examines whether the amount of time spent studying each day is linked to performance in maths exams. Along the way, you will practise collecting data, organising raw figures, calculating averages and spreads, drawing scatter diagrams, interpreting correlation and making predictions. Every step mirrors what CAIE examiners expect from a well‑structured data‑handling exercise.
本文将带你完成一个适用于九年级 CAIE 统计的完整统计调查。你将跟随一名学生，研究每天学习时长是否与数学考试成绩相关。在此过程中，你将练习收集数据、整理原始数据、计算平均数和离散程度、绘制散点图、解读相关性并进行预测。每一步都映射出 CAIE 考官对结构化数据处理练习的期望。
1. Introduction to the Case Study | 案例介绍
A Year 9 student wanted to find out whether spending more time on maths revision would lead to higher test scores. She decided to ask 30 classmates two simple questions: ‘How many hours do you usually study maths per day?’ and ‘What was your percentage score in the last maths test?’ All responses were recorded anonymously so that nobody felt pressured. This real‑life mini‑project gives us a chance to apply the statistical techniques covered in the CAIE course to a genuine set of data.
一位九年级学生想知道花更多时间复习数学是否会导致更高的考试分数。她决定向 30 位同学提出两个简单问题：“你通常每天学习数学多少小时？”以及“你上次数学测试的百分比分数是多少？”所有回答均匿名记录，以免有人感到压力。这个真实的小项目让我们有机会将 CAIE 课程中涉及的统计技术应用于一组真实数据。
2. Data Collection and Raw Data Table | 数据收集与原始数据表
The table below shows the raw data gathered from the 30 students. The study time is given in hours, and the test score is a percentage. This is the starting point for any statistical analysis – clear, organised recording of every observation.
下表显示了从 30 名学生收集的原始数据。学习时间以小时为单位，测试分数为百分比。这是任何统计分析的起点——清晰、有条理地记录每个观测值。
| Study Time (h) | Score (%) |
|---|---|
| 0.5 | 43 |
| 0.5 | 45 |
| 0.8 | 48 |
| 1.0 | 50 |
| 1.0 | 52 |
| 1.2 | 54 |
| 1.3 | 55 |
| 1.5 | 58 |
| 1.5 | 57 |
| 1.5 | 60 |
| 1.8 | 62 |
| 2.0 | 64 |
| 2.0 | 63 |
| 2.0 | 66 |
| 2.0 | 68 |
| 2.2 | 70 |
| 2.2 | 69 |
| 2.5 | 72 |
| 2.5 | 74 |
| 2.5 | 73 |
| 2.7 | 76 |
| 2.8 | 78 |
| 3.0 | 80 |
| 3.0 | 79 |
| 3.2 | 82 |
| 3.2 | 84 |
| 3.5 | 88 |
| 3.5 | 86 |
| 4.0 | 90 |
| 0.5 | 44 |
Notice that the data is ungrouped and each row pairs one study time with one score. This pairing is essential because we later want to see if a relationship exists between the two variables.
请注意，数据尚未分组，每一行将一个学习时间与一个分数配对。这种配对至关重要，因为我们随后想探究两个变量之间是否存在关系。
3. Organising the Data: Ordering and Sorting | 整理数据：排序与整理
Before calculating averages, it is helpful to sort the data in ascending order. For the study‑time variable, the ordered list becomes: 0.5, 0.5, 0.5, 0.8, 1.0, 1.0, 1.2, 1.3, 1.5, 1.5, 1.5, 1.8, 2.0, 2.0, 2.0, 2.0, 2.2, 2.
Published by TutorHao | Year 9 统计 Revision Series | aleveler.com
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