Case Study in Statistics: Practical Application and Analysis | 统计案例分析实战演练

📚 Case Study in Statistics: Practical Application and Analysis | 统计案例分析实战演练

In this article, we will explore a complete case study that demonstrates how statistical concepts are applied to real-world data. You will analyse a dataset of 30 students, including their Mathematics scores, English scores, and weekly study hours. By working through this case study, you will reinforce your understanding of descriptive statistics, correlation, regression, and probability — all essential for your Cambridge IGCSE / O Level Statistics examination.

本文将探究一个完整的案例，演示如何将统计概念应用于真实数据。你将分析一个包含 30 名学生的数据集，包括数学成绩、英语成绩和每周学习时间。通过这个案例分析，你将巩固对描述性统计、相关性、回归和概率的理解——所有这些对于你的剑桥 IGCSE / O Level 统计考试都至关重要。

1. Introducing the Case Study | 案例引入

A school conducted a survey among its Year 11 students to investigate academic performance and study habits. The data collected includes each student’s Mathematics score (out of 100), English score (out of 100), and weekly study hours. This dataset will be analysed to uncover patterns and inform teaching strategies.

某学校对 Year 11 学生进行了一项调查，以研究学业表现与学习习惯的关系。收集的数据包括每位学生的数学成绩（满分 100 分）、英语成绩（满分 100 分）以及每周学习时间（小时）。我们将分析这一数据集，以揭示规律并为教学策略提供参考。

The table below displays all 30 records. Each row represents a unique student identified by a number from 1 to 30. This raw dataset is the foundation of our statistical exploration.

下表展示了全部 30 条记录。每一行代表一名由 1 至 30 编号的学生。这个原始数据集是我们统计探索的基础。

2. Data Types and Variables | 数据类型与变量

The dataset contains three variables: Mathematics score, English score, and weekly study hours. Both test scores are discrete numerical variables because they are measured in whole marks. Study hours are continuous numerical data, as they can take any value within a reasonable range, although recorded to the nearest hour in this survey.

该数据集包含三个变量：数学成绩、英语成绩和每周学习时间。两项考试成绩都是离散数值变量，因为它们以整分计量。学习时间是连续数值数据，因为它可以在合理范围内取任意值，但在本次调查中记录为最接近的整数小时。

It is important to identify variable types correctly, as this determines which statistical measures and graphs are appropriate. For instance, we use scatter graphs for pairs of continuous or discrete data, and we calculate means and standard deviations for numerical variables.

正确识别变量类型很重要，因为这决定了哪些统计量度和图形是合适的。例如，我们对成对的连续或离散数据使用散点图，并对数值变量计算均值和标准差。

In this case study, we will treat both scores as quantitative and will not group them into categories unless we need to construct a frequency distribution. However, we might group study hours into intervals for a histogram to observe the distribution of study patterns.

在本案例中，我们将把两项成绩都视为定量数据，除非需要构建频数分布，否则不会将其分组。不过，我们可能会将学习时间分组为区间，以便绘制直方图来观察学习模式的分布。

3. Organising Data: Frequency Tables | 数据整理：频数表

To see the shape of the Mathematics scores, we can construct a grouped frequency table with class intervals of width 10. This reveals how scores are distributed across the range 0–100.

为了观察数学成绩的分布形态，我们可以构建一个组距为 10 的分组频数表。这能揭示成绩在 0–100 范围内的分布情况。

The modal class is 80–89 with a frequency of 6, indicating that more students scored in this high range than in any other interval. The cumulative frequency column helps us locate medians and quartiles later.

众数所在组为 80–89，频数为 6，这表明落入该高分段的学生多于任何其他区间。累积频数列帮助我们稍后确定中位数和四分位数。

Similarly, we could tabulate study hours using intervals of 5 hours (e.g., 0–4, 5–9, etc.). This preparation makes it easier to draw histograms or cumulative frequency curves, which are expected skills in your examination.

类似地，我们可以使用 5 小时间隔（例如 0–4、5–9 等）对学习时间制表。这一准备工作使绘制直方图或累积频数曲线更加容易，这也是考试中要求掌握的技能。

4. Measures of Central Tendency: Mean, Median, Mode | 集中趋势度量：均值、中位数、众数

The mean Mathematics score is calculated by summing all 30 values and dividing by 30:

数学平均分通过将所有 30 个数值相加再除以 30 得出：

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