📚 Case Study: Statistical Analysis in Action | 案例分析实战演练：统计应用
In Year 7 Statistics, learning how to collect, organise, display and interpret data is essential. This case study walks you through a real classroom survey to show how statistical skills are applied in practice. Follow the steps to understand the full data handling cycle.
在七年级统计中，学习如何收集、整理、展示和解读数据至关重要。本案例将带你走进一个真实的课堂调查，展示如何将统计技能应用于实际。请跟随步骤，了解完整的数据处理流程。
1. Case Background | 案例背景
A Year 7 teacher wants to understand her students’ after-school habits. She decides to conduct a survey asking two questions: ‘What is your favourite sport?’ and ‘How many minutes do you spend on homework each day?’ The data collected will be used to teach statistical methods.
一位七年级老师想了解学生的课后习惯。她决定进行一项调查，提出两个问题：“你最喜欢的运动是什么？”和“你每天花多少分钟做作业？”收集到的数据将用于教授统计方法。
The survey is anonymous, and students are encouraged to give honest answers. The class has 32 students, all of whom participate.
此次调查为匿名形式，并鼓励学生如实作答。全班共有32名学生，均参加了调查。
2. Research Questions: What Do We Want to Know? | 研究问题：我们想了解什么？
Before collecting data, it is crucial to define clear research questions. Our first question investigates students’ preferences for sports – this is categorical data. The second question examines the amount of time spent on homework – this is numerical data.
在收集数据之前，明确研究问题至关重要。第一个问题调查学生对运动的偏好——这是分类数据。第二个问题考察做作业所花的时间——这是数值数据。
Having both types of data allows us to practise a wide range of statistical techniques, from drawing charts to calculating averages and measures of spread.
拥有两种类型的数据使我们能够练习多种统计技巧，从绘制图表到计算平均数和离散度量。
3. Data Collection Method | 数据收集方法
The teacher prepares a simple questionnaire. Each student writes down their favourite sport from a list (Football, Basketball, Swimming, Tennis, Other) and the number of minutes they spent on homework the previous day. Data is collected from all 32 students in the class.
老师准备了一份简单的问卷。每个学生从列表（足球、篮球、游泳、网球、其他）中写下自己最喜欢的运动，以及前一天用于做作业的分钟数。数据收集自全班32名学生。
To ensure accuracy, students are reminded to be honest and to record the homework time as accurately as possible. They are told to round their time to the nearest 5 minutes to simplify recording.
为确保准确性，提醒学生诚实作答并尽可能准确记录作业时间。他们被告知将时间四舍五入到最接近的5分钟，以简化记录。
4. Dataset 1: Favourite Sports – Organising Categorical Data | 数据集1：最喜欢的运动——整理分类数据
Here are the raw results for favourite sports collected from 32 students: 12 chose Football, 8 Basketball, 6 Swimming, 4 Tennis and 2 selected Other. We can organise this into a frequency table.
以下是32名学生最喜欢的运动的原始结果：12人选择足球，8人篮球，6人游泳，4人网球，2人选其他。我们可以将其整理成频数表。
| Sport (运动) | Frequency (频数) |
|---|---|
| Football (足球) | 12 |
| Basketball (篮球) | 8 |
| Swimming (游泳) | 6 |
| Tennis (网球) | 4 |
| Other (其他) | 2 |
| Total (总计) | 32 |
This frequency table makes it easy to see the most and least popular sports. Football dominates with over a third of the votes, while ‘Other’ is the smallest group.
这张频数表便于我们观察最受欢迎和最不受欢迎的运动。足球以超过三分之一的票数占据主导地位，而“其他”是最小组。
5. Visualising Categorical Data: Bar Charts and Pie Charts | 可视化分类数据：条形图和饼图
A bar chart is a great way to visualise categorical data. Each sport category is displayed on the horizontal axis, and the frequency on the vertical axis. For our data, the bar for Football would be the tallest at 12, followed by Basketball at 8, Swimming at 6, Tennis at 4, and Other at 2.
条形图是可视化分类数据的绝佳方式。每个运动类别显示在横轴上，频数显示在纵轴上。对于我们的数据，足球的条形最高为12，其次是篮球8，游泳6，网球4，其他2。
For a pie chart, we need to calculate the angle for each sector. Since there are 32 students in total, each student represents 360° ÷ 32 = 11.25°. We multiply each frequency by 11.25° to get the angle.
对于饼图，我们需要计算每个扇形的角度。因为总共有32名学生，每名学生代表360° ÷ 32 = 11.25°。将每个频数乘以11.25°即可得到角度。
| Sport (运动) | Frequency (频数) | Angle (角度) |
|---|---|---|
| Football | 12 | 135° |
| Basketball | 8 | 90° |
| Swimming | 6 | 67.5° |
| Tennis | 4 | 45° |
| Other | 2 | 22.5° |
These angles are then used to draw the sectors using a protractor and compass. Always label each sector and include a title.
然后使用量角器和圆规根据这些角度画出扇形。务必给每个扇形贴上标签并加上标题。
6. Dataset 2: Daily Homework Time – Numerical Data | 数据集2：每日作业时间——数值数据
The teacher also recorded the homework minutes for a subset of 15 students to study numerical data in more depth. The raw data, rounded to the nearest 5 minutes, is: 30, 45, 60, 30, 20, 45, 60, 90, 30, 45, 60, 40, 50, 30, 60.
老师还记录了其中15名学生的作业分钟数，以便更深入地研究数值数据。原始数据（四舍五入到5分钟）为：30, 45, 60, 30, 20, 45, 60, 90, 30, 45, 60, 40, 50, 30, 60。
These values are numerical and can be ordered from smallest to largest. Arranging them gives us: 20, 30, 30, 30, 30, 40, 45, 45, 45, 50, 60, 60, 60, 60, 90.
这些值是数值型，可以从小到大排序。排序后得到：20, 30, 30, 30, 30, 40, 45, 45, 45, 50, 60, 60, 60, 60, 90。
7. Visualising Numerical Data: Dot
Published by TutorHao | Year 7 统计 Revision Series | aleveler.com
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