📚 Year 7 AQA Statistics: Case Study Practical Exercise | Year 7 AQA 统计：案例分析实战演练
Statistics is not just about numbers and formulas – it is about understanding the world through data. In this practical exercise, you will follow a complete statistical investigation from start to finish. By the end, you will know how to collect, organise, present, and interpret data just like a real statistician. Let us dive into a realistic case study that mirrors what you might encounter in your Year 7 AQA Statistics lessons.
统计学不仅仅是数字和公式，它是通过数据理解世界的方式。在这个实战演练中，你将从头到尾完成一项完整的统计调查。到最后，你将学会如何像真正的统计学家一样收集、整理、展示和解读数据。让我们深入一个贴近真实情境的案例研究，这将反映你在 Year 7 AQA 统计课上可能遇到的内容。
1. Introducing the Case Study: Favourite Lunch Choices | 案例介绍：最喜爱的午餐选择
Imagine your school canteen wants to improve its menu. To make better decisions, the staff need to know which lunch options are most popular among Year 7 students. Your task is to carry out a statistical investigation. You will design a data collection sheet, gather responses from a sample of classmates, and then analyse the results to recommend which dishes should be kept, changed, or removed.
想象一下，你的学校食堂想要改进菜单。为了做出更好的决定，工作人员需要了解 Year 7 学生最喜爱哪些午餐选择。你的任务是开展一项统计调查。你将设计一份数据收集表，从一部分同学那里收集回答，然后分析结果，建议哪些菜品应该保留、调整或移除。
2. Types of Data and Data Collection | 数据类型与数据收集
First, we need to decide what kind of data we are collecting. The variable “favourite lunch choice” can be recorded as categories like ‘Pasta’, ‘Chicken Wrap’, ‘Salad’, ‘Pizza’, or ‘Jacket Potato’. This is categorical data (specifically, nominal data) because the answers are names, not numbers that can be measured.
首先，我们需要决定要收集哪种类型的数据。变量“最喜爱的午餐选择”可以记录为类别，如“意大利面”、“鸡肉卷”、“沙拉”、“披萨”或“烤土豆”。这是分类数据（具体为名义数据），因为答案都是名称，而不是可以测量的数字。
To collect the data efficiently, you prepare a simple table with tally marks. You ask 30 Year 7 students: “What is your favourite lunch option?” Each response is recorded with a tally stroke. Grouping the strokes in fives makes counting easier later.
为了高效地收集数据，你准备了一个简单的表格并采用画记法。你询问了 30 名 Year 7 学生：“你最喜爱的午餐选择是什么？”每个回答用一条画记记录。将画记每五个一组，这样便于以后计数。
3. Organising the Raw Data into a Frequency Table | 将原始数据整理为频数表
After collecting all the responses, you count the tally marks and convert them into frequencies. Here is the completed frequency table for our case study:
收集完所有回答后，你清点画记并将其转化为频数。下面是本案例完整的频数表：
| Lunch Option (午餐选择) | Tally (画记) | Frequency (频数) |
|---|---|---|
| Pasta (意大利面) | |||| | 4 |
| Chicken Wrap (鸡肉卷) | |||| |||| | 10 |
| Salad (沙拉) | || | 2 |
| Pizza (披萨) | |||| || | 7 |
| Jacket Potato (烤土豆) | |||| || | 7 |
Always check that the total frequency adds up to the number of students asked. Here, 4 + 10 + 2 + 7 + 7 = 30, so the data is consistent.
一定要检查总频数是否等于被询问的学生人数。这里，4 + 10 + 2 + 7 + 7 = 30，所以数据是一致的。
4. Presenting Data with a Bar Chart | 用条形图展示数据
A bar chart is a great way to compare the frequencies of different categories. Each bar represents one lunch option, and the height of the bar shows its frequency. The bars do not touch because the data is categorical, not continuous.
条形图是比较不同类别频数的绝佳方式。每一个条形代表一种午餐选择，条形的高度表示其频数。条形之间不相连，因为数据是分类数据，而非连续数据。
When drawing the bar chart, remember to label both axes: the horizontal axis is “Lunch Option” and the vertical axis is “Frequency”. Use an appropriate scale so the tallest bar fits comfortably. The bar for Chicken Wrap would be the highest at 10, while Salad is the lowest at 2.
绘制条形图时，记得给两条轴都加上标签：横轴为“午餐选择”，纵轴为“频数”。选择合适的刻度，让最高的条形也能轻松容纳。鸡肉卷的条形会是最高的，达到10，而沙拉的条形最低，仅为2。
5. Creating a Pie Chart to Show Proportions | 制作饼图展示比例
To show what fraction of the group chose each option, we use a pie chart. The whole circle represents all 30 students (360°). We calculate the angle for each sector by using the formula:
为了展示每个选项所占的比例，我们使用饼图。整个圆代表全部 30 名学生（360°）。我们用以下公式计算每个扇区的角度：
Sector angle = (Frequency / Total frequency) × 360°
扇区角度 = （频数 / 总频数） × 360°
For example, for Pasta with a frequency of 4, the angle is (4 ÷ 30) × 360° = 48°. For Chicken Wrap: (10 ÷ 30) × 360° = 120°. For Salad: (2 ÷ 30) × 360° = 24°. Pizza and Jacket Potato both have 7, so each gets (7 ÷ 30) × 360° = 84°. Check that the angles sum to 360°.
例如，意大利面的频数为4，角度为（4 ÷ 30）× 360° = 48°。鸡肉卷：（10 ÷ 30）× 360° = 120°。沙拉：（2 ÷ 30）× 360° = 24°。披萨和烤土豆的频数都是7，所以每个的角度为（7 ÷ 30）× 360° = 84°。检查角度总和是否为360°。
6. Calculating Averages: Mean, Median, and Mode | 计算平均数：均值、中位数和众数
Although this data is categorical, sometimes we assign numerical codes or consider the frequency itself. For practice, we can calculate the mean, median, and mode of the frequency distribution to understand central tendency in a different context. Here, we treat the frequencies as a small data set: 4, 10, 2, 7, 7.
虽然这些数据是分类数据，但有时我们会赋予数值代码或考虑频数本身。为了练习，我们可以计算这组频数分布的均值、中位数和众数，以在不同情境中理解集中趋势。这里，我们将频数视为一个小的数据集：4, 10, 2, 7, 7。
First, order the values: 2, 4, 7, 7, 10. The mode is the most frequent value, which is 7 (it appears twice). The median is the middle value: the third value in the ordered list is 7. The mean is the sum of all frequencies divided by the number of categories: (4+10+2+7+7) ÷ 5 = 30 ÷ 5 = 6.
首先，将数值排序：2, 4, 7, 7, 10。众数是出现最频繁的值，即7（出现了两次）。中位数是中间值：排序后第三位是7。均值是所有频数之和除以类别数：（4+10+2+7+7）÷ 5 = 30 ÷ 5 = 6。
In a real scenario for the canteen, the modal lunch choice is Chicken Wrap with a frequency of 10, which tells us that more students prefer this option than any other.
在食堂的真实情境中，最喜爱的午餐选择的众数是鸡肉卷，频数为10，这告诉我们喜欢这个选项的学生比任何其他选项都多。
7. Understanding the Range and Variability | 了解极差与变异性
The range tells us the spread of our frequency data. Range = largest value – smallest value. From the frequency set (4, 10, 2, 7, 7), the largest frequency is 10 and the smallest is 2, so the range is 10 – 2 = 8. This shows a big difference in the popularity of lunch options.
极差告诉我们频数数据的分散程度。极差 = 最大值 – 最小值。从频数集合（4, 10, 2, 7, 7）中，最大频数是10，最小频数是2，因此极差为 10 – 2 = 8。这表明午餐选择之间的受欢迎程度差异很大。
In the canteen context, a large range means some items are much more popular than others. This information can help the canteen staff decide to keep the popular items and perhaps replace the least popular ones.
在食堂情境下，极差较大意味着某些菜品比其他菜品受欢迎得多。这些信息可以帮助食堂工作人员决定保留受欢迎的菜品，并可能替换掉最不受欢迎的菜品。
8. Interpreting the Results and Drawing Conclusions | 解读结果并得出结论
Based on our analysis, Chicken Wrap is the clear favourite, with a frequency of 10 out of 30. Pizza and Jacket Potato are also quite popular, each chosen by 7 students. Pasta has a moderate following, while Salad is rarely selected. The canteen should consider offering Chicken Wrap more often, keeping Pizza and Jacket Potato as regular options, and perhaps running a special promotion for Pasta or a revised salad recipe.
根据我们的分析，鸡肉卷明显是最受欢迎的，30人中有10人选择。披萨和烤土豆也相当受欢迎，各有7名学生选择。意大利面有一定的支持者，而沙拉很少有人选。食堂应考虑更经常地提供鸡肉卷，保留披萨和烤土豆作为常规选项，或许可以对意大利面进行特别推广，或改进沙拉食谱。
Always check if your conclusions make sense and are supported by the data. Avoid making claims beyond what the numbers show. For instance, we cannot say that every Year 7 student will love Chicken Wrap, because our sample is only 30 students.
一定要检查你的结论是否合理且有数据支持。避免做出超出数据范围的断言。例如，我们不能说每一个 Year 7 学生都会喜欢鸡肉卷，因为我们的样本只有30名学生。
9. Evaluating the Investigation and Possible Improvements | 评估调查与可能的改进
Every statistical investigation has limitations. Our sample size of 30 is reasonable but could be larger to better represent all Year 7 students. Also, the question only allowed one favourite choice; some students might have liked two options equally. We could improve by asking students to rank their top three choices or by collecting data from more tutor groups. Another improvement would be to record the data by gender or form class to see if preferences differ.
每项统计调查都有局限性。我们30人的样本量是合理的，但可以更大一些，以更好地代表所有 Year 7 学生。此外，问题只允许选择一个最喜爱的选项；有些学生可能同样喜欢两个选项。我们可以通过要求学生排列前三名选择，或者从更多的导师组收集数据来改进。另一个改进是按性别或班级记录数据，看看偏好是否有所不同。
10. Linking to AQA Statistics Skills for Year 7 | 对接 Year 7 AQA 统计技能
This case study exercise covers several key skills from the Year 7 AQA Statistics specification: distinguishing between types of data, designing data collection sheets, using tally charts, constructing frequency tables, drawing bar charts and pie charts, calculating the mean of a set of numbers, finding the mode and median, and calculating the range. It also emphasises interpretation and evaluation, which are crucial for achieving higher marks.
本案例练习涵盖了 Year 7 AQA 统计学课程中的几项关键技能：区分数据类型、设计数据收集表、使用画记表、构建频数表、绘制条形图和饼图、计算一组数的均值、找出众数和中位数，以及计算极差。它还强调了数据解读与评估，这对于取得高分至关重要。
By working through a complete investigation, you are better prepared for the types of structured questions that ask you to plan, represent, and reason statistically.
通过完成一项完整的调查，你能更好地应对那些要求你进行统计规划、表示和推理的结构化问题。
Published by TutorHao | Statistics Revision Series | aleveler.com
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