Case Study in Statistics: Hands-On Practice for Year 7 OCR | 案例分析实战演练

📚 Case Study in Statistics: Hands-On Practice for Year 7 OCR | 案例分析实战演练

In this revision guide, we will walk through a complete statistical case study based on a school canteen survey. You will practice every step of a real investigation – from designing a questionnaire to drawing conclusions. By working through these hands-on exercises, you will strengthen your skills for the Year 7 OCR Statistics paper and learn how data helps make better decisions in everyday life.

本复习指南将通过一个基于学校食堂调查的完整统计案例，带你逐步演练一项真实调查的每一步——从设计问卷到得出结论。通过这些实操练习，你将巩固针对 Year 7 OCR 统计学的各项技能，并了解数据如何在日常生活中帮助人们做出更好的决策。

1. Understanding the Case Study: School Canteen Survey | 理解案例：学校食堂调查

Our school canteen manager wants to find out if students are happy with the current menu. The goal is to collect opinions from Year 7 pupils about their favourite meal types, any complaints about waiting times, and suggestions for new dishes. The results will help the canteen plan a revised menu for next term.

我们学校食堂经理想了解学生对当前菜单是否满意。目标是收集七年级学生对最喜欢餐食类型、对等候时间的抱怨以及新菜品建议等意见。调查结果将帮助食堂规划下学期的修订菜单。

This is a typical statistical investigation. You will need to identify what data to collect, how to gather it fairly, and then organise, present and interpret the results. Start by writing down the main question: ‘What changes would improve the Year 7 canteen experience?’

这是一项典型的统计调查。你需要明确要收集哪些数据、如何公平地收集数据，然后对结果进行整理、呈现和解读。首先写下主要问题：“哪些改变可以改善七年级的食堂体验？”

2. Collecting Data: Designing a Questionnaire | 收集数据：设计问卷

A well-designed questionnaire is key to collecting useful data. We need questions that are clear, not leading, and give a good mix of response options. For the canteen survey, we might ask: ‘Which meal type do you prefer?’ with options Pizza, Pasta, Salad, Wraps, Hot meals. We should also ask about waiting time: ‘How long do you usually queue? Less than 5 min, 5-10 min, More than 10 min’.

精心设计的问卷是收集有用数据的关键。我们需要问题清晰、不带引导性，并提供合理的选项组合。针对食堂调查，我们可以问：“你更喜欢哪种餐食类型？”选项为披萨、意面、沙拉、卷饼、热餐。我们还应询问等候时间：“你通常排队多长时间？少于5分钟、5-10分钟、超过10分钟”。

It is important to test the questionnaire on a small group first to spot confusing wording. We also decide to survey a random sample of 50 Year 7 students during form time to avoid bias. You should always record responses carefully, using a clipboard or a digital form.

重要的是先在一小群人中测试问卷，以发现令人困惑的措辞。我们还决定在辅导时间随机抽取50名七年级学生进行调查，以避免偏差。记录回答时一定要仔细，可以使用写字板或电子表单。

3. Organising Data with Tally Charts | 用划记表整理数据

Once the questionnaires are returned, raw data must be organised. A tally chart is a quick way to count frequencies. For the meal preference question, draw a table with three columns: Meal type, Tally, Frequency. Use groups of five (four vertical marks crossed by a diagonal) to make counting easier.

问卷收回后，必须整理原始数据。划记表是快速统计频数的方法。对于餐食偏好问题，绘制一个三列表格：餐食类型、划记、频数。采用五条一组（四竖一横）的方式让计数更简便。

After tallying, you might get frequencies like: Pizza IIII IIII (9), Pasta IIII I (6), Salad III (3), Wraps IIII II (7), Hot meals IIII IIII I (11). There were 50 students in total, but here the sum is 36, which means some answers were missing or marked ‘Other’. Always check totals.

划记后，你可能得到这样的频数：披萨 IIII IIII (9), 意面 IIII I (6), 沙拉 III (3), 卷饼 IIII II (7), 热餐 IIII IIII I (11)。总共调查了50名学生，但这里总和是36，意味着有些回答缺失或被归为“其他”。一定要检查总数。

4. Displaying Data: Bar Charts and Pictograms | 展示数据：条形图和象形图

A bar chart is perfect for showing frequencies of different categories. On the x-axis, put the meal types; on the y-axis, put frequency from 0 up to at least 12. Draw bars of equal width with gaps between them. Always label axes and give the chart a title, for example ‘Year 7 Favourite Meal Types’.

条形图非常适合展示不同类别的频数。x 轴标注餐食类型，y 轴标注频数，从 0 至少到 12。绘制等宽柱体且柱间留空隙。务必标注坐标轴并为图表加上标题，例如“七年级最爱餐食类型”。

A pictogram could also be used, where each symbol represents 2 students. For Pizza (9 students), use 4 and a half symbols. Make sure to include a key showing what one symbol stands for. Pictograms help younger audiences understand data quickly.

也可以使用象形图，每个符号代表2名学生。对于披萨（9名学生），使用4个半符号。确保图例说明每个符号的含义。象形图能帮助年龄较小的读者快速理解数据。

5. Averages: Calculating the Mean | 平均数：计算平均值

The mean is the ‘average’ you get by adding up all the values and dividing by how many there are. In our survey, we asked students how many minutes they spent queuing each day: 8, 12, 5, 9, 7, 11, 6, 10, 4, 13 (sample of 10). Find the mean waiting time.

平均值（均数）是将所有数值相加再除以数值的个数得到的“平均数”。在我们的调查中，我们询问了学生每天排队花费的分钟数：8, 12, 5, 9, 7, 11, 6, 10, 4, 13（10人样本）。求平均等候时间。

Sum = 8+12+5+9+7+11+6+10+4+13 = 85 minutes
Mean = 85 ÷ 10 = 8.5 minutes

总和 = 8+12+5+9+7+11+6+10+4+13 = 85 分钟
平均值 = 85 ÷ 10 = 8.5 分钟

The mean queuing time is 8.5 minutes. Remember the mean can be affected by very high or very low values. Always round sensibly when reporting.

平均排队时间为8.5分钟。记住，平均值可能会受极高或极低数值的影响。汇报结果时要合理取整。

6. Median and Mode: Finding the Middle and Most Frequent | 中位数和众数：找中间和最频繁的

The median is the middle value when data is ordered. For the same queuing times: order them – 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. With an even number of values, the median is the mean of the two middle numbers (8 and 9), so (8+9)÷2 = 8.5 minutes. Notice here the mean and median are the same.

中位数是将数据排序后位于中间的值。对于同一组排队时间：排序——4, 5, 6, 7, 8, 9, 10, 11, 12, 13。数据个数为偶数时，中位数为中间两个数（8 和 9）的平均值，即 (8+9)÷2 = 8.5 分钟。请注意，这里的平均值和中位数相同。

The mode is the most frequent value. In the set above, no number repeats, so there is no mode. However, from our whole-year waiting time data, we might find that ‘5 minutes’ appears most often. Then 5 minutes would be the mode, telling us the typical queue time experienced by many.

众数是出现次数最多的值。在上述数据集中，没有重复数字，因此没有众数。但从我们整个年级的等候时间数据中，我们可能发现“5分钟”出现最多。那么5分钟就是众数，它反映了许多学生经历的典型排队时间。

7. The Range: Measuring Spread | 范围：衡量离散程度

The range shows how spread out the data is. It is calculated as: Range = Highest value – Lowest value. For our 10 queuing times, range = 13 – 4 = 9 minutes. A large range means waiting times vary a lot from student to student.

范围（极差）显示数据的离散程度。计算公式为：范围 = 最大值 – 最小值。对于我们的10个排队时间，范围 = 13 – 4 = 9 分钟。范围较大意味着不同学生的等待时间差异很大。

When comparing two datasets, the range helps you see consistency. If the Year 8 queue times had a range of 4 minutes, their experience is more predictable. Always mention range alongside an average to give a fuller picture of the data.

在比较两个数据集时，范围可以帮助你了解一致性。如果八年级排队时间的范围是4分钟，他们的体验就更可预测。在报告平均值时同时提及范围，能更全面地呈现数据全貌。

8. Interpreting Pie Charts from the Canteen Data | 解读食堂数据的饼图

A pie chart can show how the whole sample is divided into meal preferences as proportions. To draw a pie chart, you need to calculate the angle for each sector. For Pizza with 9 out of 36 valid responses, the fraction is 9/36 = 1/4. Multiply by 360° to get 90°.

饼图可以展示整个样本如何按餐食偏好划分成不同比例。要绘制饼图，你需要计算每个扇形的角度。对于披萨，在36份有效回答中占9份，比例为9/36 = 1/4。乘以360°得到90°。

Calculate other angles: Pasta 6/36 × 360° = 60°, Salad 3/36 × 360° = 30°, Wraps 7/36 × 360° ≈ 70°, Hot meals 11/36 × 360° ≈ 110°. Always check that angles sum to 360°. Now label each sector with the meal type and percentage.

计算其他角度：意面 6/36 × 360° = 60°，沙拉 3/36 × 360° = 30°，卷饼 7/36 × 360° ≈ 70°，热餐 11/36 × 360° ≈ 110°。务必检查角度总和是否为360°。然后给每个扇形标注餐食类型和百分比。

Pie charts are excellent for showing proportions, but they are harder to read exact frequencies from. Bar charts still rule when you need precise counts.

饼图在展示比例方面非常出色，但从中读出精确频数较困难。当你需要精确计数时，条形图仍然是首选。

9. Comparing Data Sets: Before and After Menu Change | 比较数据集：菜单变更前后

After analysing the survey, the canteen introduced a new menu with more wrap choices and a faster ‘grab-and-go’ counter. A second survey was done with another 50 students. We can compare the mean queue times.

在分析调查结果后，食堂推出了新菜单，增加了更多卷饼选择并设置了一个快速“即取即走”柜台。又对另外50名学生进行了第二次调查。我们可以比较平均排队时间。

Original mean queue time = 8.5 min, range = 9 min. New survey mean = 5.2 min, range = 6 min. This suggests the changes reduced both the average wait and the variation in wait times. You can display the two sets of data using dual bar charts or back-to-back stem-and-leaf diagrams.

初次调查平均排队时间 = 8.5 分钟，范围 = 9 分钟。新调查平均值 = 5.2 分钟，范围 = 6 分钟。这表明采取的措施既降低了平均等待时间，也缩小了等待时间的变化。你可以使用双条形图或背靠枝叶图来展示这两组数据。

When comparing, always comment on both an average and a measure of spread. Use phrases like ‘On average, queue times dropped by 3.3 minutes, and the experience became more consistent for students.’

做比较时，务必同时评论一种平均值和一种离散度量。使用类似这样的表述：“平均而言，排队时间减少了3.3分钟，且学生的体验变得更加一致了。”

10. Spotting Outliers and Anomalies | 发现离群值和异常

An outlier is a value that lies far outside the rest of the data. In our original queue times, if one student reported a wait of 25 minutes, this would be an outlier. It might be an error, or it could be a genuine extreme case (perhaps someone joined the lunch queue very late).

离群值是远偏离数据中其他值的数值。在我们最初的排队时间数据中，如果有一名学生报告等待了25分钟，这就是一个离群值。这可能是一个错误，也可能是一个真实的极端情况（也许有人很晚才加入午间排队）。

You should always investigate outliers. Check the original questionnaire: maybe the student wrote ‘2-5 min’ and you misread it. If it is a real value, you need to decide whether to include it in calculations – it can pull the mean up dramatically, so the median might be a better average to report.

你应该始终调查离群值。检查原始问卷：也许该学生写的是“2-5分钟”，而你误读了。如果它是一个真实值，你需要决定是否将其纳入计算——它可能会大幅拉高平均值，因此报告中位数可能是更好的平均量数。

11. Drawing Conclusions and Making Recommendations | 得出结论和提出建议

The final step is to go back to the original question: ‘What changes would improve the Year 7 canteen experience?’ Based on the data, we can conclude that hot meals and pizza are most popular, but many students want faster service. The grab-and-go counter reduced mean waiting time from 8.5 to 5.2 minutes.

最后一步是回到最初的问题：“哪些改变会改善七年级的食堂体验？”根据数据，我们可以得出结论：热餐和披萨最受欢迎，但许多学生希望服务更快。即取即走柜台将平均等候时间从8.5分钟降低到5.2分钟。

Our recommendation is to keep the hot meal and pizza options, continue the express counter, and perhaps run another survey to include more salad options for the students who chose ‘Other’. Always be specific and support recommendations with numbers from your analysis.

我们的建议是保留热餐和披萨选项，继续提供快速柜台，并可以再进行一次调查，为选择“其他”的学生增加更多沙拉选项。提出建议时要具体，并用分析中的数字作为依据。

12. Review: Key Skills Check | 复习：关键技能检查

Let’s quickly check the core statistical skills we have practiced in this case study. Can you:

让我们快速回顾一下我们在这个案例中练习的核心统计技能。你能否做到：

Design a simple, unbiased questionnaire with closed and open questions?

设计一份简单、无偏见的问卷，包含封闭式与开放式问题？
Use tally charts to organise raw data and calculate frequencies?

使用划记表整理原始数据并计算频数？
Draw and label bar charts, pie charts and pictograms?

绘制并标注条形图、饼图和象形图？
Calculate the mean, identify the median and mode from a data set?

计算平均值，并从数据集中找出中位数和众数？
Compute the range and explain what it tells you about consistency?

计算范围，并解释它告诉你怎样的数据一致性？
Compare two data sets using averages and range?

使用平均值和范围比较两个数据集？
Spot and deal with outliers?

发现并处理离群值？
Write a conclusion that answers the investigation question and gives evidence-based recommendations?

撰写结论，回答调查问题并提出基于证据的建议？

If you can say ‘yes’ to all of these, you are well prepared for your Year 7 OCR Statistics assessment. Practise with friends, collect your own data, and turn everyday questions into mini investigations. Good luck!

如果你对以上所有问题都能回答“是”，那么你已经为 Year 7 OCR 统计学测评做好了充分准备。和朋友一起练习，收集你自己的数据，把日常问题变成小型调查。祝你好运！

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Case Study in Statistics: Hands-On Practice for Year 7 OCR | 案例分析实战演练