📚 Year 7 CIE Statistics: Case Study Practice | Year 7 CIE 统计：案例分析实战演练
In Year 7 CIE Statistics, applying your knowledge to real-life situations is the best way to master data handling. This article presents three complete case studies, guiding you through every step from defining a question to drawing conclusions. By working through these practical examples, you will strengthen your understanding of averages, charts, and data interpretation.
在七年级CIE统计课程中，将知识应用到实际场景是掌握数据处理的最佳方法。本文提供了三个完整的案例研究，带你走完从定义问题到得出结论的每一步。通过实践这些案例，你将加深对平均数、图表和数据解释的理解。
1. What is a Statistical Case Study? | 什么是统计案例分析？
A statistical case study uses real or realistic data to explore a specific question. It involves collecting, organising, displaying and analysing information to uncover patterns or answer practical questions. Instead of simply memorising formulas, you learn how statistics helps make decisions in everyday life.
统计案例分析利用真实或模拟数据来探索特定问题。它包括收集、整理、展示和分析信息，以发现模式或回答实际问题。你不再只是死记硬背公式，而是学习如何运用统计知识在日常生活中做决策。
Think of a school survey about favourite subjects or measuring the growth of plants over a month – these are small case studies where you play the role of a data detective. Throughout this article you will step into that role and solve three mini-investigations.
想一想学校关于最喜爱科目的调查，或者测量植物在一个月内的生长情况——这些都是小型的案例研究，你将扮演数据侦探的角色。在本文中，你将进入这个角色，完成三个小型调查。
2. The Data Handling Cycle | 数据处理循环
Every statistical case study follows a cycle: Pose a question → Collect data → Organise data → Display data → Analyse and draw conclusions. Knowing this cycle helps you work systematically and avoid missing important steps.
每一个统计案例研究都遵循一个循环：提出问题 → 收集数据 → 整理数据 → 展示数据 → 分析并得出结论。了解这个循环有助于你有条理地工作，避免遗漏重要步骤。
For example, if you want to know ‘How tall are the Year 7 students in my school?’, you must first decide how to measure and record heights, then collect the values, sort them, draw a graph, compute averages and finally state what you have found.
例如，如果你想知道“我学校的七年级学生有多高？”，你需要先决定如何测量并记录身高，然后收集数值，排序，绘制图表，计算平均数，最后陈述你的发现。
3. Step 1: Pose a Real Question | 第一步：提出真实问题
A clear question gives your investigation focus. Good statistical questions are specific, measurable and relevant. Instead of asking ‘Are students healthy?’, ask ‘What is the average number of hours Year 7 students sleep on a school night?’ The second question can be answered with numbers.
一个明确的问题能让你的调查有重点。好的统计问题应当是具体的、可量化的且相关的。与其问“学生们健康吗？”，不如问“七年级学生在上学日的晚上平均睡多少小时？”第二个问题可以用数字来回答。
In our first case study we ask: What is the typical height of a Year 7 student in Class 7A? This lets us plan exactly what data to collect.
在我们的第一个案例中，我们问：七年级A班学生的典型身高是多少？ 这让我们能准确计划需要收集哪些数据。
4. Step 2: Collect the Data | 第二步：收集数据
Data can be collected by taking measurements, conducting surveys, or using existing records. It is important to record data accurately and note the units. For the height study, we use a tape measure to record each student’s height to the nearest centimetre.
数据可以通过测量、调查或使用现有记录来收集。准确记录数据并注明单位非常重要。在身高研究中，我们用卷尺测量每个学生的身高，精确到最接近的厘米。
We also need to decide on the sample. Here we will measure all 10 students in Class 7A. A clear table with two columns – student name and height – is a simple way to record the raw data before any calculations.
我们还需要决定样本。这里我们将测量A班的全部10名学生。使用一个清晰的表格，包含两列——学生姓名和身高——是进行任何计算前记录原始数据的简单方法。
5. Case Study A: Heights of Year 7 Students | 案例A：七年级学生身高
The heights (in cm) of the 10 students in Class 7A are: 150, 155, 148, 162, 157, 150, 163, 148, 155, 160. These numbers look a bit messy, so the next job is to sort them from smallest to largest: 148, 148, 150, 150, 155, 155, 157, 160, 162, 163.
A班10名学生的身高（厘米）为：150, 155, 148, 162, 157, 150, 163, 148, 155, 160。这些数字看起来有些杂乱，所以下一步是将它们从小到大排序：148, 148, 150, 150, 155, 155, 157, 160, 162, 163。
Sorting the data makes it much easier to find the median and to spot any values that repeat. We can already see that 148 and 150 each appear twice, as do 155 – this gives us a hint about the mode.
将数据排序后，更容易找到中位数，也更容易发现任何重复的数值。我们已经看到148和150各出现两次，155也是如此——这为众数提供了线索。
6. Computing the Mean, Median, Mode and Range | 计算平均数、中位数、众数和范围
To find the mean, add all the heights and divide by the number of students.
要计算平均数，将所有身高相加，然后除以学生人数。
Mean = (148 + 148 + 150 + 150 + 155 + 155 + 157 + 160 + 162 + 163) ÷ 10 = 1548 ÷ 10 = 154.8 cm
平均数 = (148 + 148 + 150 + 150 + 155 + 155 + 157 + 160 + 162 + 163) ÷ 10 = 1548 ÷ 10 = 154.8 厘米
The median is the middle value. With 10 values, the median lies between the 5th and 6th numbers in the sorted list: 155 and 155. So the median is (155 + 155) ÷ 2 = 155 cm.
中位数是中间值。有10个数时，中位数位于排序列表的第5和第6个数之间：155和155。因此中位数为(155 + 155) ÷ 2 = 155厘米。
The mode is the most frequent value. Here 148, 150 and 155 each appear twice, so the data set is multi-modal with modes 148 cm, 150 cm and 155 cm.
众数是出现次数最多的数值。这里148、150和155各出现两次，因此这组数据是多众数的，众数为148厘米、150厘米和155厘米。
The range = maximum – minimum = 163 – 148 = 15 cm. This tells us how spread out the heights are.
极差 = 最大值 – 最小值 = 163 – 148 = 15厘米。它告诉我们身高的分布范围有多宽。
7. Interpreting Height Data | 解读身高数据
The mean (154.8 cm) and median (155 cm) are very close, which suggests the heights are fairly symmetric and not skewed by extreme values. The range of 15 cm shows that all students fall within a relatively narrow band of heights.
平均数（154.8厘米）和中位数（155厘米）非常接近，这表明身高分布相当对称，没有受到极端值的偏斜。15厘米的极差显示所有学生的身高都在一个相对较窄的范围内。
If a new student joined the class with a height of 180 cm, the mean would increase noticeably, but the median might only shift slightly. This demonstrates why the median is often a better measure of central tendency when there are outliers.
如果有一名身高180厘米的新生加入班级，平均数会明显增加，但中位数可能只略微移动。这说明了为什么当存在异常值时，中位数通常是更好的集中趋势度量。
8. Case Study B: Favourite Colours Survey | 案例B：最喜欢的颜色调查
Now we move from numerical data to categorical data. A survey asked 30 students: ‘What is your favourite colour?’ The results are: Red: 8, Blue: 12, Green: 5, Yellow: 3, Other: 2.
现在我们从数值型数据转移到分类型数据。一项调查询问了30名学生：“你们最喜欢的颜色是什么？”结果是：红色：8，蓝色：12，绿色：5，黄色：3，其他：2。
Categorical data cannot be averaged like heights, but we can still find the mode (most popular colour) and display the frequencies in charts. The mode here is Blue, with 12 votes.
分类数据不能像身高那样求平均数，但我们仍然可以找到众数（最受欢迎的颜色）并用图表展示频数。这里的众数是蓝色，有12票。
We can organise the data into a frequency table:
我们可以将数据整理成一个频数表：
| Colour | Frequency |
|---|---|
| Red | 8 |
| Blue | 12 |
| Green | 5 |
| Yellow | 3 |
| Other | 2 |
9. Drawing Bar Charts and Pie Charts | 绘制条形图和饼图
A bar chart uses bars of equal width; the height of each bar represents the frequency. For our colour data, the blue bar would be the tallest (12 units), followed by red (8), green (5), yellow (3) and other (2). You must label both axes and give the chart a title.
条形图使用等宽的条形；每个条形的高度代表频数。对于我们的颜色数据，蓝色的条形最高（12个单位），其次是红色（8），绿色（5），黄色（3）和其他（2）。你必须给两条坐标轴添加标签，并给图表加上标题。
A pie chart shows the same information as slices of a circle. Each slice’s angle is calculated using the formula: (frequency ÷ total) × 360°. For blue, the angle is (12 ÷ 30) × 360° = 144°. The other angles are: Red 96°, Green 60°, Yellow 36° and Other 24°. Once drawn, each slice should be labelled or a key provided.
饼图把相同的信息显示为圆形切片。每个切片的角度用公式计算：(频数 ÷ 总数) × 360°。蓝色：(12 ÷ 30) × 360° = 144°。其他角度：红色96°，绿色60°，黄色36°，其他24°。绘制后，每个切片应标注或提供图例。
Comparing the two charts, the bar chart makes it very easy to read exact frequencies, while the pie chart quickly shows the proportion of each colour relative to the whole.
比较两种图表，条形图很容易读出精确的频数，而饼图则能快速显示每种颜色相对于整体的比例。
10. Case Study C: Travel Time to School | 案例C：上学通勤时间
Our last case study looks at the time (in minutes) 12 students take to travel to school. The data collected are: 10, 15, 12, 20, 18, 25, 10, 30, 22, 15, 12, 18.
最后一个案例研究是12名学生上学所花的时间（分钟）。收集到的数据为：10, 15, 12, 20, 18, 25, 10, 30, 22, 15, 12, 18。
Again, sorting helps: 10, 10, 12, 12, 15, 15, 18, 18, 20, 22, 25, 30. We can calculate the mean: (10+10+12+12+15+15+18+18+20+22+25+30) ÷ 12 = 207 ÷ 12 = 17.25 minutes.
排序再次带来帮助：10, 10, 12, 12, 15, 15, 18, 18, 20, 22, 25, 30。我们可以计算平均数：(10+10+12+12+15+15+18+18+20+22+25+30) ÷ 12 = 207 ÷ 12 = 17.25分钟。
The median is between the 6th (15) and 7th (18) values: (15 + 18) ÷ 2 = 16.5 minutes. The mode includes 10, 12, 15 and 18 (each appears twice) – so the data again have multiple modes. The range is 30 – 10 = 20 minutes.
中位数在第6个（15）和第7个（18）数值之间：(15 + 18) ÷ 2 = 16.5分钟。众数包括10、12、15和18（各出现两次）——因此数据再次是多众数的。极差为30 – 10 = 20分钟。
11. Stem-and-Leaf Diagrams for Travel Time | 通勤时间的茎叶图
A stem-and-leaf diagram is a quick way to show shape and spread while keeping the original data. The ‘stem’ represents the tens digit; the ‘leaf’ is the units digit. For example, 15 minutes gives a stem of 1 and leaf of 5.
茎叶图是一种快速展示数据分布形态和分散程度的方法，同时保留原始数据。“茎”表示十位数，“叶”是个位数。例如，15分钟的茎是1，叶是5。
Our sorted travel times displayed as a stem-and-leaf diagram:
我们排序后的通勤时间用茎叶图显示如下：
Stem (tens) | Leaf (units)
1 | 0 0 2 2 5 5 8 8
2 | 0 2 5
3 | 0
The diagram shows most students take between 10 and 18 minutes, with a few taking over 20 minutes. There is a gap between 22 and 30 minutes, and one student takes 30 minutes – which could be considered an outlier if it were much larger than the rest.
该图显示大多数学生花10到18分钟，少数超过20分钟。在22和30分钟之间存在一个间隙，有一名学生花了30分钟——如果这个值远大于其他数据，可以看作是异常值。
12. Comparing All Three Cases and Drawing Conclusions | 比较三个案例并得出结论
Across the three case studies we have practised the full data handling cycle. With numerical data (heights and travel times), we calculated mean, median, mode and range and learned when each measure is most useful. With categorical data (colours), we used frequency tables and charts to summarise findings.
通过这三个案例研究，我们练习了完整的数据处理循环。对于数值型数据（身高和通勤时间），我们计算了平均数、中位数、众数和极差，并了解了每种度量何时最有用。对于分类型数据（颜色），我们使用频数表和图表来总结发现。
Key lessons include: always sort your data before finding the median; the mode is the only average for categorical data; the range gives a quick sense of variation; and diagrams like stem-and-leaf plots help you see patterns instantly. By connecting calculations to real questions, you turn raw numbers into meaningful stories.
关键的收获包括：在找中位数之前始终先排序；众数是分类数据的唯一平均数度量；极差能快速反映变异程度；像茎叶图这样的图表能帮助你立即看到模式。通过将计算与真实问题联系起来，你将原始数字转化为有意义的故事。
Published by TutorHao | Statistics Revision Series | aleveler.com
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