📚 Year 9 CCEA Statistics: Case Study Practical Exercises | 九年级CCEA统计：案例分析实战演练
In Year 9 CCEA Statistics, one of the most powerful ways to build confidence is through case study practical exercises. This article walks you through a realistic data investigation – from designing a survey to presenting conclusions. You will see how raw data becomes useful information and then have the chance to work through a practice exercise of your own.
在九年级CCEA统计课程中，通过案例分析实战练习是建立信心的最有效方式之一。本文将带你走过一个真实的数据调查过程——从设计问卷到展示结论。你将看到原始数据如何变成有用的信息，然后有机会自己完成一个练习。
1. Designing a Survey | 设计调查问卷
Before collecting any data, you need a clear question. For our case study, we want to find out: “What are the favourite lunch options and weekly canteen visit patterns of Year 9 students?” The survey must be simple and anonymous to encourage honest answers.
在收集任何数据之前，你需要一个清晰的问题。在我们的案例中，我们想了解：“九年级学生最喜欢的午餐选择以及每周去食堂的频次模式是怎样的？”问卷必须简单且匿名，以鼓励诚实回答。
We will ask two questions: 1) Which meal do you prefer? (Pizza, Burger, Salad, Pasta) 2) How many times do you visit the canteen per week? (record a whole number).
我们会问两个问题：1）你更喜欢哪一种餐点？（披萨、汉堡、沙拉、意面）2）你每周去食堂多少次？（记录一个整数）。
Good surveys avoid leading or confusing wording. Always test your questions on a friend before distributing them.
好的问卷避免诱导性或令人困惑的措辞。在分发之前，先让朋友测试一下你的问题。
2. Collecting the Data | 收集数据
We surveyed 30 Year 9 students during form time. Data collection must be organised: each response was recorded in a table with columns for Student ID, Favourite Meal and Weekly Visits.
我们在班会时间调查了30名九年级学生。数据收集必须有条理：每个回答都记录在一个表格中，包含学生编号、最喜欢的餐点和每周访问次数。
Here is the raw data we obtained. Favourite meal: Pizza (12 students), Burger (8), Salad (6), Pasta (4). Weekly visits: 3, 4, 2, 5, 4, 3, 2, 4, 5, 3, 4, 2, 5, 3, 4, 3, 2, 5, 4, 3, 4, 5, 3, 2, 4, 3, 5, 4, 3, 4.
这是我们获得的原始数据。最喜欢的餐点：披萨（12名学生），汉堡（8名），沙拉（6名），意面（4名）。每周访问次数：3, 4, 2, 5, 4, 3, 2, 4, 5, 3, 4, 2, 5, 3, 4, 3, 2, 5, 4, 3, 4, 5, 3, 2, 4, 3, 5, 4, 3, 4。
Always check your data for errors, such as impossible numbers or missing values. In this dataset, all values are valid.
务必检查数据中的错误，例如不可能的数字或缺失值。在这个数据集中，所有值都是有效的。
3. Organising Data with Frequency Tables | 用频数表整理数据
For categorical data like favourite meal, a frequency table shows how many students chose each option. This makes it easier to spot the most and least popular items.
对于类别数据如最喜欢的餐点，频数表显示有多少学生选择了每个选项。这使得最容易和最不受欢迎的项目一目了然。
| Meal | Frequency |
|---|---|
| Pizza | 12 |
| Burger | 8 |
| Salad | 6 |
| Pasta | 4 |
| Total | 30 |
For the numerical data (weekly visits), a frequency table groups the numbers. Let’s list each distinct value and count how many times it appears.
对于数值数据（每周访问次数），频数表将数字分组。让我们列出每个不同的值并统计它出现的次数。
| Weekly visits | Frequency |
|---|---|
| 2 | 6 |
| 3 | 10 |
| 4 | 10 |
| 5 | 4 |
| Total | 30 |
Notice that the total frequency must equal the number of data points collected. This is a quick accuracy check.
请注意，总频数必须等于收集的数据点数。这是一个快速的准确性检查。
4. Visualising Data: Bar Chart and Pie Chart | 数据可视化：条形图和饼图
A bar chart is perfect for comparing favourite meals. Each category has a bar whose height represents the frequency. The pizza bar would be the tallest at 12.
条形图非常适合比较最喜欢的餐点。每个类别都有一个柱子，其高度代表频数。披萨的柱子最高，为12。
For the same categorical data, a pie chart shows proportions. Pizza takes up 12/30 = 0.4 of the circle, which is 40%. Burger is 8/30 ≈ 27%, Salad 20%, Pasta 13%.
对于相同的类别数据，饼图显示比例。披萨占圆的12/30 = 0.4，即40%。汉堡约占27%，沙拉20%，意面13%。
When drawing charts by hand, always label axes and provide a title. For the bar chart, the x-axis is ‘Meal’ and y-axis ‘Frequency’. For the pie chart, calculate each angle: Pizza 144°, Burger 96°, Salad 72°, Pasta 48°.
手工绘制图表时，务必标记坐标轴并提供标题。条形图的x轴是“餐点”，y轴是“频数”。饼图中，计算每个角度：披萨144°，汉堡96°，沙拉72°，意面48°。
5. Visualising Numerical Data: Dot Plot | 数值数据可视化：点图
For the weekly visits data, a dot plot is a simple way to see the distribution. Place a number line from 2 to 5 and stack a dot for each student above their visit count.
对于每周访问次数数据，点图是观察分布的简单方法。画一条从2到5的数轴，并在每个访问次数上方堆叠一个点来表示每位学生。
You would see clusters at 3 and 4, with fewer students visiting 2 or 5 times. A dot plot quickly reveals the mode (most frequent value) which here are 3 and 4 (bimodal).
你会看到在3和4处有聚集点，访问2次或5次的学生较少。点图能够快速揭示众数（最频繁的值），这里是3和4（双峰）。
6. Calculating Averages: Mean, Median, Mode | 计算平均数：均值、中位数、众数
The mean is the sum of all weekly visits divided by the number of students. Sum = 2×6 + 3×10 + 4×10 + 5×4 = 12 + 30 + 40 + 20 = 102. Mean = 102 ÷ 30 = 3.4 visits per week.
均值是所有每周访问次数的总和除以学生人数。总和 = 2×6 + 3×10 + 4×10 + 5×4 = 12 + 30 + 40 + 20 = 102。均值 = 102 ÷ 30 = 3.4次每周。
The median is the middle value when data are ordered. With 30 values, the median lies between the 15th and 16th values. Ordered list: six 2s, ten 3s, ten 4s, four 5s. The 15th and 16th are both 4, so median = 4.
中位数是数据排序后的中间值。有30个数据，中位数位于第15和第16个值之间。排序列表：六个2，十个3，十个4，四个5。第15和16个都是4，所以中位数 = 4。
The mode is the most common number. Here, both 3 and 4 appear ten times, so the data is bimodal with modes 3 and 4.
众数是最常见的数字。这里，3和4都出现了十次，因此数据是双峰的，众数为3和4。
For the categorical meal data, the mode is Pizza because it has the highest frequency (12). Mean and median are not meaningful for categorical data.
对于类别餐点数据，众数是披萨，因为它频数最高（12）。对于类别数据，均值和中位数没有意义。
7. Measuring Spread: Range | 测量离散程度：极差
The range tells you how spread out the data are. For weekly visits, range = maximum – minimum = 5 – 2 = 3. This indicates that the number of visits varies by up to 3 days per week across the class.
极差告诉你数据的分散程度。对于每周访问次数，极差 = 最大值 – 最小值 = 5 – 2 = 3。这表明全班每周访问次数的差异最多为3天。
A small range means students are fairly consistent in canteen visits; a large range would suggest very different habits. Always report the range alongside a measure of centre to give a full picture.
极差小意味着学生在食堂访问上相当一致；极差大则暗示习惯差异很大。报告极差时应同时报告一个集中趋势指标，以提供全貌。
8. Introduction to Probability from Data | 从数据引入概率
Using our frequency data, we can estimate probabilities. If you pick a Year 9 student at random, the probability they prefer Pizza is 12/30 = 0.4 (or 40%). Probability (Burger) = 8/30 ≈ 0.267.
利用我们的频数数据，我们可以估算概率。如果随机选择一名九年级学生，他们更喜欢披萨的概率是12/30 = 0.4（或40%）。概率（汉堡） = 8/30 ≈ 0.267。
Similarly, the probability of visiting the canteen more than 3 times per week is the number of students visiting 4 or 5 times divided by 30: (10+4)/30 = 14/30 ≈ 0.467.
类似地，每周访问食堂超过3次的概率是访问4次或5次的学生人数除以30：（10+4）/30 = 14/30 ≈ 0.467。
Always express probability as a fraction, decimal or percentage. These experimental probabilities are based on our sample and can be used to make predictions about the whole year group if the sample is representative.
始终将概率表示为分数、小数或百分数。这些实验概率基于我们的样本，如果样本具有代表性，可以用来对整个年级进行预测。
9. Interpreting Results and Drawing Conclusions | 解释结果并得出结论
From the analysis, we see that Pizza is the most popular meal, and the typical student visits the canteen about 3 to 4 times a week. The range of visits is small, indicating similar habits across the class.
从分析中我们看到，披萨是最受欢迎的餐点，典型学生每周去食堂约3到4次。访问次数的极差较小，表明全班的习惯相似。
To improve the canteen, the school might consider offering more Pizza days while also promoting healthier options like Salad, since only 20% chose it.
为了改善食堂，学校可以考虑增加披萨供应的天数，同时也推广更健康的选择如沙拉，因为只有20%的学生选择了它。
Always link conclusions back to the original question and acknowledge any limitations. Our sample was only 30 students from one class; a larger sample would give more reliable results.
始终将结论联系回原始问题，并承认任何局限性。我们的样本只来自一个班级的30名学生；更大的样本会给出更可靠的结果。
10. Practice Exercise: Design Your Own Case Study | 实战练习：设计你自己的案例研究
Now it is your turn. Conduct a mini survey on a topic of your choice, such as “Number of hours spent on homework per week” or “Favourite sports”. Collect data from at least 20 classmates.
现在轮到你了。就你选择的主题进行一个迷你调查，例如“每周花在作业上的小时数”或“最喜欢的运动”。从至少20名同学那里收集数据。
Complete these steps: 1) Write a clear survey question. 2) Collect and record data neatly. 3) Draw a frequency table for categorical or numerical data. 4) Create a suitable chart (bar chart, pie chart or dot plot). 5) Calculate mean, median, mode and range if numerical. 6) Write a short paragraph explaining what the data shows.
完成以下步骤：1）写一个清晰的调查问题。2）整齐地收集并记录数据。3）为类别或数值数据画频数表。4）创建合适的图表（条形图、饼图或点图）。5）如果是数值数据，计算均值、中位数、众数和极差。6）写一小段话解释数据所显示的内容。
Suggested topics: favourite fruit, travel time to school, number of books read in a month. Be creative but ensure the data can be counted or measured.
建议主题：最喜欢的水果、上学通勤时间、一个月内读的书的数量。要有创意，但确保数据是可计数或可测量的。
11. Common Mistakes and Tips | 常见错误与提示
Mistake 1: Forgetting to total frequencies – always check that the sum matches the number of respondents. Mistake 2: Confusing mean and median – remember the median is the middle value, not the average.
错误1：忘记总计频数——始终检查总和是否与受访者数量一致。错误2：混淆均值和中位数——记住中位数是中间值，不是平均数。
Mistake 3: Drawing charts without labels or titles – always name the axes and give a title. Mistake 4: Calculating range incorrectly – it is max minus min, not max plus min.
错误3：绘制图表时没有标签或标题——务必命名坐标轴并给出标题。错误4：错误计算极差——它是最大值减最小值，而不是最大值加最小值。
Tip: Use coloured pens to make your charts clear. Double-check calculations using a calculator. When writing conclusions, say “On average…” or “The data suggests…” to sound professional.
提示：使用彩色笔让你的图表清晰。用计算器双重检查计算。在写结论时，说“平均而言……”或“数据表明……”以显得专业。
12. Summary: Why Case Studies Matter | 总结：为什么案例研究很重要
Working through a case study helps you turn theory into practical skills. You learn not only how to calculate but also how to think statistically – asking questions, gathering evidence, analysing and communicating findings.
完成一个案例研究有助于你将理论转化为实践技能。你不仅学会如何计算，还学会如何统计思考——提出问题、收集证据、分析并沟通发现。
These skills are at the heart of CCEA Statistics and prepare you for real-world situations where data drives decisions. Keep practising with different datasets to become a confident statistical investigator.
这些技能是CCEA统计的核心，并为你应对数据驱动决策的真实情境做好准备。继续用不同的数据集练习，成为一名自信的统计调查者。
Published by TutorHao | Statistics Revision Series | aleveler.com
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