AQA Year 9 Statistics: School Canteen Survey Case Study | AQA 九年级统计：学校食堂调查案例实战

📚 AQA Year 9 Statistics: School Canteen Survey Case Study | AQA 九年级统计：学校食堂调查案例实战

This practical case study walks you through a full statistical investigation, from designing a questionnaire to drawing conclusions using probability. It mirrors the tasks you might tackle in your Year 9 AQA Statistics course, developing your skills in data handling, presentation and interpretation.

本实战案例将带你完成一个完整的统计调查过程，从设计问卷到运用概率得出结论。它模拟了你可能在九年级 AQA 统计课程中遇到的任务，帮助你培养数据处理、呈现与解释的技能。

1. Introduction to the Case Study | 案例介绍

The school leadership team wants to find out how satisfied Year 9 students are with the canteen. Your statistics class has been asked to carry out a formal investigation. You will need to design a survey, collect a sample, organise the data, present it clearly and calculate summary statistics and probabilities.

学校领导团队希望了解九年级学生对食堂的满意度。你们的统计班被要求进行一次正式的调查。你需要设计问卷、抽取样本、整理数据、清晰地呈现数据，并计算概括性统计量和概率。

The brief is to produce a report that includes at least two types of chart, averages for a numerical variable, a scatter graph to explore a possible relationship and simple probability statements based on the data.

任务要求是制作一份报告，其中至少包含两种图表、一个数值变量的平均数、一张探索可能关系的散点图以及基于数据的简单概率陈述。

---

2. Designing the Questionnaire | 设计调查问卷

Before collecting any data you must decide what to ask and how to ask it. The questions need to be clear, unbiased and easy to answer. For this investigation two closed questions are chosen.

在收集数据之前，你必须决定要问什么以及如何提问。问题必须清晰、无偏见且容易回答。本次调查选择了两道封闭式问题。

Question 1: ‘How satisfied are you with the school canteen overall?’ The response options use a five-point scale: Very satisfied, Satisfied, Neutral, Dissatisfied, Very dissatisfied.

问题 1：”你对学校食堂的整体满意度如何？” 回答选项采用五点量表：非常满意、满意、一般、不满意、非常不满意。

Question 2: ‘How many days in a typical week do you buy food or drink from the canteen?’ The response is a whole number from 0 to 5 because the canteen is open five days a week.

问题 2：”在一周中，你通常有几天会从食堂购买食物或饮料？” 回答是从 0 到 5 的整数，因为食堂每周开放五天。

An optional open-ended question could gather suggestions, but for the statistical tasks only the closed responses are used so that numerical analysis is possible.

还可以设置一道可选的开放式问题以收集建议，但统计任务仅使用封闭式回答，以便进行数值分析。

---

3. Sampling Method | 抽样方法

It is impossible to ask every student in the school, so you need to choose a sample. A simple random sample of 50 Year 9 students is selected using a random number generator on the year group list. This gives every student an equal chance of being chosen and reduces selection bias.

不可能询问学校里的每一位学生，因此你需要选择一个样本。使用随机数生成器从九年级名单中抽取了 50 名学生的简单随机样本。这使每位学生都有相同的被选中的机会，并减少了选择偏差。

Sampling from only Year 9 is a judgement made because the investigation focuses on that year group. If we wanted to generalise to the whole school, a stratified sample by year group would be more appropriate.

只从九年级抽样是基于调查对象的判断。如果我们想将结论推广到全校，按年级分层抽样会更合适。

All 50 questionnaires were returned fully completed, giving a response rate of 100% and a clean dataset to work with.

发出的 50 份问卷全部完整回收，回复率为 100%，得到了一个干净的数据集。

---

4. Collecting and Organising Data | 数据收集与整理

The collected data are summarised into two frequency tables. The first table shows satisfaction levels, and the second shows the number of canteen visits per week.

收集到的数据汇总为两个频数表。第一个表展示满意度水平，第二个表展示每周去食堂的次数。

Satisfaction frequency table:

满意度频数表：

Satisfaction level	Frequency
Very satisfied	10
Satisfied	15
Neutral	12
Dissatisfied	8
Very dissatisfied	5
Total	50

Canteen visits per week frequency table:

每周食堂就餐次数频数表：

Number of visits	Frequency
5	8
4	10
3	15
2	9
1	5
0	3
Total	50

Both tables show that every response fits into exactly one category, making the data suitable for bar charts, pie charts and other calculations.

两张表都表明每份回答恰好归入一个类别，因此数据适合绘制条形图、饼图并进行其他计算。

---

5. Data Presentation: Bar Chart | 数据呈现：条形图

A bar chart is ideal for displaying categorical data like satisfaction levels. The horizontal axis shows the five satisfaction categories, and the vertical axis shows frequency. Each bar is drawn with equal width and a gap between bars to emphasise that the categories are separate.

条形图非常适合展示满意度水平这类分类数据。横轴显示五类满意度，纵轴表示频数。每个条形宽度相同，条与条之间有间隔，以突出类别是相互独立的。

From the satisfaction table, the bar for ‘Satisfied’ is the tallest at 15, followed by ‘Neutral’ at 12, ‘Very satisfied’ at 10, ‘Dissatisfied’ at 8 and ‘Very dissatisfied’ at 5. The chart makes it easy to see at a glance that most students feel neutral or better, while a minority are dissatisfied.

从满意度表中可以看到，”满意” 的条形最高，为 15，其次是 “一般” 12，”非常满意” 10，”不满意” 8，”非常不满意” 5。这张图让人一眼就能看出大多数学生感觉一般或更好，而少数学生不满意。

The bar chart can be drawn by hand on graph paper, ensuring the axes are labelled and a title is provided, such as ‘Year 9 Students’ Satisfaction with the School Canteen’.

可以在坐标纸上手绘条形图，确保坐标轴有标签并写上标题，例如 “九年级学生对学校食堂的满意度”。

---

6. Data Presentation: Pie Chart | 数据呈现：饼图

A pie chart shows proportions. To construct it, multiply each fraction (frequency ÷ total) by 360° to find the sector angle.

饼图展示各部分所占比例。绘制时，用每个分数（频数 ÷ 总数）乘以 360° 得到扇形角度。

Calculations for the satisfaction pie chart:

满意度饼图的角度计算：

Very satisfied: 10/50 × 360° = 72°

非常满意：10/50 × 360° = 72°

Satisfied: 15/50 × 360° = 108°

满意：15/50 × 360° = 108°

Neutral: 12/50 × 360° = 86.4°

一般：12/50 × 360° = 86.4°

Dissatisfied: 8/50 × 360° = 57.6°

不满意：8/50 × 360° = 57.6°

Very dissatisfied: 5/50 × 360° = 36°

非常不满意：5/50 × 360° = 36°

Check that the total sums to 72° + 108° + 86.4° + 57.6° + 36° = 360°, confirming no mistake. Using a protractor, each sector is drawn in turn, starting from a vertical radius.

检查总和：72° + 108° + 86.4° + 57.6° + 36° = 360°，确认无误。使用量角器，从一条垂直半径开始，依次画出各个扇形。

The ‘Satisfied’ slice occupies the largest angle, while ‘Very dissatisfied’ is the smallest. The pie chart reinforces that more than half the students chose a positive category.

“满意” 部分的扇形角度最大，”非常不满意” 则最小。饼图再次强调，超过一半的学生选择了正面类别。

---

7. Calculating Mean, Median, Mode and Range | 计算平均数、中位数、众数和极差

For the numerical data on canteen visits per week, we can find the mean, median, mode and range. These measures summarise the typical number of visits and the spread.

对于每周食堂就餐次数这一数值型数据，我们可以求出平均数、中位数、众数和极差。这些量度概括了典型的就餐次数及其分散程度。

First, calculate the total number of visits: (5 × 8) + (4 × 10) + (3 × 15) + (2 × 9) + (1 × 5) + (0 × 3) = 40 + 40 + 45 + 18 + 5 + 0 = 148.

首先，计算总次数：(5 × 8) + (4 × 10) + (3 × 15) + (2 × 9) + (1 × 5) + (0 × 3) = 40 + 40 + 45 + 18 + 5 + 0 = 148。

The mean is total visits divided by the number of students: 148 ÷ 50 = 2.96 visits per week.

平均数为总次数除以学生人数：148 ÷ 50 = 2.96 次/周。

To find the median, list the visits in order and find the middle value. With 50 students, the median lies between the 25th and 26th values. Cumulative frequencies: 5 visits: 8 (positions 1-8), 4 visits: 10 (positions 9-18), 3 visits: 15 (positions 19-33). Both the 25th and 26th values are 3, so the median is 3.

为了求中位数，将次数排序并找到中间值。50 名学生，中位数位于第 25 和第 26 个值之间。累积频数：5 次：8（第 1-8 位），4 次：10（第 9-18 位），3 次：15（第 19-33 位）。第 25 和第 26 个值都是 3，因此中位数为 3。

The mode is the most frequent number of visits. With a frequency of 15, 3 visits occurs most often, so the mode is 3.

众数是出现次数最多的就餐次数。频数为 15 的 3 次出现得最频繁，因此众数是 3。

The range is the difference between the highest and lowest values. Highest visits = 5, lowest = 0, so the range = 5 – 0 = 5 visits.

极差是最大值与最小值之差。最高次数 = 5，最低 = 0，因此极差 = 5 – 0 = 5 次。

Summary: The typical Year 9 student visits the canteen about 3 times a week, but there is considerable variation, with some students never buying anything.

小结：典型的九年级学生每周去食堂约 3 次，但存在较大差异，有些学生从不购买任何东西。

---

8. Scatter Graphs and Correlation | 散点图与相关性

We can also explore whether students who visit the canteen more often tend to be more satisfied. Each student’s data gives a pair: number of visits and a satisfaction score (Very satisfied = 5, Satisfied = 4, Neutral = 3, Dissatisfied = 2, Very dissatisfied = 1).

我们还可以探讨，更常光顾食堂的学生是否往往更满意。每位学生的数据构成一个数对：就餐次数和满意度评分（非常满意 = 5，满意 = 4，一般 = 3，不满意 = 2，非常不满意 = 1）。

Plot these 50 points on a scatter graph with ‘number of visits’ on the horizontal axis and ‘satisfaction score’ on the vertical axis. Draw a line of best fit through the points.

将 50 个点画在散点图上，横轴为 “就餐次数”，纵轴为 “满意度评分”。画一条通过各点的最佳拟合线。

From the plot, you might notice that points with higher visit numbers tend to have higher satisfaction scores. This suggests a weak positive correlation. It could mean that students who enjoy the canteen go there more, or that frequent visitors are more satisfied with what is on offer.

从图中你可能注意到，就餐次数较高的点往往有较高的满意度评分，这暗示存在弱正相关。这可能意味着喜欢食堂的学生去得更勤，或者常客更满意食堂提供的食物。

Remember that correlation does not imply causation, but the scatter graph helps to visualise a possible relationship between two variables.

请记住，相关并不意味着因果关系，但散点图有助于可视化两个变量之间可能存在的关系。

---

9. Basic Probability: Probability of Random Selection | 概率基础：随机选择的概率

Using the satisfaction frequency table, you can calculate the probability of different outcomes if one student is chosen at random from the sample of 50.

利用满意度频数表，你可以计算从 50 名样本中随机选择一名学生时不同结果的概率。

The probability of an event = number of favourable outcomes ÷ total number of outcomes.

事件概率 = 有利结果的数量 ÷ 总结果数量。

Probability the student is ‘Very satisfied’ = 10/50 = 1/5 or 0.2.

被选中的学生 “非常满意” 的概率 = 10/50 = 1/5 或 0.2。

Probability the student is either ‘Dissatisfied’ or ‘Very dissatisfied’ = (8 + 5)/50 = 13/50 = 0.26.

学生 “不满意” 或 “非常不满意” 的概率 = (8 + 5)/50 = 13/50 = 0.26。

Probability the student is at least ‘Satisfied’ (i.e. Satisfied or Very satisfied) = (15 + 10)/50 = 25/50 = 1/2 = 0.5.

学生至少 “满意”（即满意或非常满意）的概率 = (15 + 10)/50 = 25/50 = 1/2 = 0.5。

A probability of 0.5 means that if we picked a student at random many times, we would expect about half of them to be in the satisfied groups. The total of all probabilities for the five categories must equal 1 (10/50 + 15/50 + 12/50 + 8/50 + 5/50 = 50/50 = 1).

概率 0.5 意味着，如果我们多次随机选取学生，预计大约有一半属于满意类。五个类别的概率之和必须等于 1（10/50 + 15/50 + 12/50 + 8/50 + 5/50 = 50/50 = 1）。

These probability statements can help the school leadership understand how likely different responses are, and they form part of a complete statistical report.

这些概率陈述能帮助学校领导了解不同回答的可能性，它们构成完整统计报告的一部分。

---

10. Conclusion and Reflection | 结论与反思

The investigation shows that overall satisfaction with the canteen is moderate: half of the students rate it as satisfied or very satisfied, while around a quarter are dissatisfied. The average number of visits is just under three per week, and there is a slight positive correlation between visits and satisfaction.

调查显示，食堂整体满意度为中等水平：半数学生评价为满意或非常满意，约四分之一不满意。平均每周就餐次数略低于三次，且就餐次数与满意度之间存在轻微正相关。

The investigation has limitations. Only Year 9 students were surveyed, so the results cannot be safely applied to other year groups. A simple random sample within Year 9 was used, but a stratified sample across all years would give a fuller picture.

本次调查有局限性。仅调查了九年级学生，因此结果不能可靠地推广到其他年级。虽然在九年级内使用了简单随机抽样，但若跨所有年级进行分层抽样，将获得更全面的情况。

Completing this case study has shown how statistical techniques work together: designing a fair questionnaire, organising raw data into tables, choosing appropriate charts, calculating averages and range, exploring relationships with scatter graphs and quantifying uncertainty with probability. These are the fundamental skills assessed in the AQA Year 9 statistics course.

完成这个案例展示了统计技术如何协同运作：设计公平的问卷、将原始数据整理成表格、选择合适的图表、计算平均数和极差、用散点图探索关系以及用概率量化不确定性。这些都是 AQA 九年级统计课程中评估的基本技能。

---

Published by TutorHao | Statistics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）