📚 Year 8 SQA Statistics: Case Study Practice | Year 8 SQA 统计：案例分析实战演练
Statistics is not just about memorising formulas – it is about investigating the world around us. In this case study, we follow a Year 8 class as they design and carry out a real survey on favourite lunch foods. You will see how statistical thinking moves step by step from a curious question to clear conclusions.
统计学不只是记公式，更是对我们周围世界的探究。在这个案例分析中，我们跟随一个Year 8班级，看他们如何设计并完成一项关于“最喜欢的午餐食物”的问卷调查。你将看到统计思维怎样从好奇的问题一步步走向清晰的结论。
1. Formulating a Statistical Question | 制订统计问题
Every statistical investigation begins with a good question. A well‑formulated statistical question anticipates variability and can be answered using data. Instead of asking ‘Do you like pizza?’, the class asked: ‘What is the most popular lunch food among pupils in our year group?’ This question allows for multiple categories and can be answered by collecting and analysing data.
每一次统计调查都从一个好问题开始。一个设计得当的统计问题能够预见数据的变异性，并可以通过收集数据来回答。这个班级没有问“你喜欢披萨吗？”，而是提出：“在我们年级组里，最受欢迎的午餐食物是什么？”这个问题允许多个类别的出现，并能通过收集和分析数据来回答。
2. Planning Data Collection | 计划数据收集
Once the question was settled, the pupils discussed how to gather data fairly. They decided to use a simple questionnaire with a list of five common lunch options: sandwiches, pasta, chicken nuggets, salad and pizza. They agreed to survey all 80 students in the year group to avoid bias, making it a census rather than a sample. Each pupil would tick only one favourite food.
问题确定后，同学们讨论了如何公平地收集数据。他们决定使用一份简单的问卷，列出五种常见的午餐选项：三明治、意面、鸡块、沙拉和披萨。他们同意对年级组里全部80名学生进行调查以避免偏差，这就构成了一次普查而不是抽样。每名学生只能勾选一种最喜欢的食物。
3. Collecting and Recording Data | 数据收集与记录
The class collected data during morning registration and used a tally chart to record responses. A tally mark was made for each vote, and every fifth mark was drawn as a diagonal line crossing the previous four to create a group of five. This made counting much faster and reduced mistakes. The final tallies for each food were counted carefully by two pupils for accuracy.
班级在早晨注册时间收集了数据，并用记数表记录回答。每得一票就画一条记数线，每第五条线画成斜线穿过前四条，形成一个“五”的组。这样做让计数更快，也减少了错误。最后由两名学生仔细清点了每种食物的最终频数以确保准确。
4. Organising Data: Frequency Table | 整理数据：频数表
The tallies were turned into a neat frequency table, a key tool for organising raw data. The table listed each food category alongside its tally and final frequency. This arrangement made it easy to see at a glance which food was most and least popular.
记数结果被整理成一张清晰的频数表，这是整理原始数据的关键工具。表格列出了每种食物类别，旁边是该类别的记数和最终频数。这样的布局让人一眼就能看出哪种食物最受欢迎，哪种最不受欢迎。
Frequency Table of Favourite Lunch Foods
| Food | Tally | Frequency |
|---|---|---|
| Sandwiches | IIII IIII | 9 |
| Pasta | IIII IIII IIII | 14 |
| Chicken nuggets | IIII IIII IIII IIII III | 23 |
| Salad | IIII II | 7 |
| Pizza | IIII IIII IIII II | 17 |
| Total | 70 |
中文对照：午餐食物频数表，显示三明治9票、意面14票、鸡块23票、沙拉7票、披萨17票，总计70人参与（当天有10人缺席）。
5. Drawing a Bar Chart | 绘制条形图
A bar chart was chosen to display the frequencies visually. The class drew the food categories on the horizontal axis and the frequency on the vertical axis. Each bar was drawn with a uniform width and a gap between bars to show that the data are categorical, not continuous. A clear title and labelled axes were added to make the chart self‑explanatory. The height of each bar directly represented the number of votes.
大家选择用条形图来直观展示频数。班级把食物类别放在横轴上，频数放在纵轴上。每个条形的宽度一致，条与条之间保持间隙，以表明数据是分类数据而非连续数据。他们加上了清晰的标题和轴标签，使图表一目了然。每个条形的高度直接对应得票数。
6. Creating a Pie Chart | 绘制饼图
To show proportions, the class also constructed a pie chart. They calculated the angle for each sector using the formula: Angle = (Frequency / Total) × 360°. For chicken nuggets, the angle was (23/70)×360° ≈ 118°. A protractor and compass were used to draw the slices accurately, and each sector was coloured differently and labelled with the food name and percentage. The pie chart made it obvious that chicken nuggets accounted for about a third of all preferences.
为了展示比例，班级还制作了饼图。他们用公式计算每个扇区的角度：角度 = (频数 ÷ 总数) × 360°。鸡块部分的角度为 (23/70)×360° ≈ 118°。他们用半圆规和圆规精确地绘制了各个扇区，并为每个部分涂上不同颜色，标注食物名称和百分比。饼图清楚地显示出鸡块约占所有偏好的三分之一。
7. Calculating Averages: Mean, Median and Mode | 计算平均值：均值、中位数和众数
Although the data are categorical, the class turned the frequency into a numerical list of position values to practise calculating averages. They used the frequencies as numbers: 9, 14, 23, 7, 17. The mode, the most frequently occurring value, was 23 (chicken nuggets). To find the median, they sorted the numbers: 7, 9, 14, 17, 23. The middle value was 14. The mean was calculated as:
尽管数据是分类数据，班级仍把频数转化为一组位置值的数字列表来练习计算平均值。他们使用的频数数字为：9、14、23、7、17。众数，即出现次数最多的值，是23（鸡块）。为了找中位数，他们将数字排序：7、9、14、17、23，中间值是14。均值计算如下：
Mean = (9 + 14 + 23 + 7 + 17) ÷ 5 = 70 ÷ 5 = 14
So the mean frequency was 14. The averages helped describe a typical level of popularity across the items. More importantly, the mode directly answered the statistical question: chicken nuggets were the most popular.
因此均值是14。这些平均值帮助描述了各项食物受欢迎程度的典型水平。更重要的是，众数直接回答了统计问题：鸡块是最受欢迎的。
8. Measuring Spread: Range | 测量离散程度：范围
To measure how spread out the preferences were, the class calculated the range. The highest frequency was 23 and the lowest was 7. The range = 23 – 7 = 16. A larger range would have meant much more variation in popularity, while a smaller range would have meant the foods were similarly popular. Here, the range of 16 pointed to a clear favourite and a clear least favourite.
为了衡量偏好的分散程度，班级计算了范围。最高频数是23，最低是7。范围 = 23 – 7 = 16。范围越大说明受欢迎程度的差异越大，范围越小则说明各食物的受欢迎程度比较接近。这里16的范围表明存在一个明显的热门选项和一个明显的冷门选项。
9. Exploring Basic Probability | 探索概率基础
The class extended the investigation by asking: ‘If we pick a pupil at random, what is the probability their favourite is pasta?’ The experimental probability is found using the formula: P(pasta) = (Frequency of pasta) / (Total frequency). From the table, P(pasta) = 14/70 = 1/5. They wrote this as 0.2 or 20%. This simple calculation showed how frequency data can be used to estimate chances, linking descriptive statistics to probability.
班级进一步探究：“如果我们随机选一名学生，他最喜欢的食物是意面的概率有多大？”实验概率用公式：P(意面) = 意面频数 ÷ 总频数。从表中得，P(意面) = 14/70 = 1/5。他们把这个概率写成0.2或20%。这一简单计算展示了如何用频数数据来估计可能性，把描述性统计和概率联系了起来。
10. Drawing Conclusions and Presenting Results | 得出结论并展示结果
Finally, the class summarised their findings. They stated that chicken nuggets were the most popular lunch food among Year 8 pupils, while salad was the least popular. The range of 16 confirmed a strong preference spread. They presented their work on a poster with the frequency table, bar chart, pie chart and summary statistics. The pupils also reflected that the missing 10 students might slightly affect the results – a limitation worth noting in any real investigation.
最后，班级总结了他们的发现。他们指出鸡块是Year 8学生中最受欢迎的午餐食物，而沙拉是最不受欢迎的。16的范围证实了偏好的强烈差异。他们在一张海报上展示了成果，包括频数表、条形图、饼图和总结统计量。学生们还反思到，缺席的10名学生可能会对结果有轻微影响——这是任何真实调查中都值得注意的局限性。
Published by TutorHao | Statistics Revision Series | aleveler.com
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