📚 Year 8 CCEA Statistics Case Study Practical Workshop | CCEA 八年级统计：案例分析实战演练
Welcome to a practical workshop designed to build real confidence in Year 8 statistics by working through extended case studies. Instead of learning skills in isolation, you will follow three complete investigations from start to finish – collecting data, choosing the right diagrams, calculating averages, drawing conclusions and reflecting on what the numbers really mean. Each case study mirrors the style of CCEA classroom tasks and end‑of‑topic assessments, helping you think like a statistician.
欢迎来到实战工作坊！我们将通过完整的案例研究，系统提升八年级统计技能。你不会再孤立地学习概念，而是跟随三个真实调查，从数据收集、选取合适的图表，到计算平均数、得出结论并反思数字背后的含义。每个案例都贴近 CCEA 课堂任务和单元测评的风格，帮助你像统计员一样思考。
1. Setting the Scene – What Makes a Good Statistical Investigation? | 做好准备——好的统计调查包含哪些环节？
Every investigation in CCEA Statistics begins with a clear question. We call this the ‘aim’. A good aim is specific and can be answered with data. Next you need to plan how to collect that data, organise it into tables or graphs, summarise it with averages and spread, and then interpret the results in plain English. In this workshop we walk through three full cycles of the statistical enquiry process.
CCEA 统计学中的每一项调查都从一个清晰的问题开始，我们称之为“目标”。好的目标具体明确，能用数据回答。然后你需要规划如何收集数据、将其整理为表格或图表、用平均数和离散程度概括数据，最后用简洁的语言解读结果。本次工作坊将带你走过完整的统计探究循环，共计三个案例。
2. Case Study 1 – School Canteen Choices | 案例研究一——学校食堂选择
Our first investigation focuses on student food preferences at a school canteen. The head of catering wants to know which meal deals are most popular so that enough stock can be ordered and waste can be reduced. Year 8 pupils are asked to design a survey and analyse the results.
第一个调查关注学生在学校食堂的食物偏好。餐饮主管想知道哪些套餐最受欢迎，以便合理订货、减少浪费。八年级学生需要设计一份问卷并分析结果。
3. Collecting the Data – Tally Charts and Question Design | 收集数据——划记表和问题设计
We design a simple tick‑box questionnaire listing five meal deals: Chicken Wrap, Veggie Pasta, Fish Fingers, Jacket Potato and Sandwich Platter. A total of 80 Year 8 students are surveyed during registration. We record responses using a tally chart. Tallies are grouped in fives (IIII) to make counting faster. The raw data is then converted into a frequency table.
我们设计了一份简单的勾选问卷，列出五种套餐：鸡肉卷、蔬菜意面、炸鱼条、烤土豆和三明治拼盘。共有 80 名八年级学生在晨会时接受了调查。我们使用划记表记录回答。划记按五条一组（IIII），便于快速计数。原始数据随即被转换为频数表。
| Meal Deal | Tally | Frequency |
|---|---|---|
| Chicken Wrap | IIII IIII IIII | 15 |
| Veggie Pasta | IIII IIII II | 12 |
| Fish Fingers | IIII IIII IIII IIII | 20 |
| Jacket Potato | IIII IIII III | 13 |
| Sandwich Platter | IIII IIII IIII IIII | 20 |
The table shows that Fish Fingers and Sandwich Platter are joint favourites, each chosen by 20 students. We double‑check the total: 15+12+20+13+20 = 80, which matches our sample size. This is a vital checking step.
表格显示，炸鱼条和三明治拼盘并列最受欢迎，各有 20 人选择。我们核对了总数：15+12+20+13+20=80，与样本量相符。这是一个关键的检查步骤。
4. Displaying Canteen Data – Bar Charts and Pie Charts | 展示食堂数据——条形图和饼图
A bar chart is the natural choice for categorical data like meal choices. The height of each bar represents the frequency. We label the horizontal axis with the meal names and the vertical axis with frequency, using a scale that goes up to at least 20. The bars are separated by equal gaps because the categories are not ordered numbers.
条形图是展示像餐食选择这类分类数据的自然选择。每个条形的高度代表频数。我们在横轴上标注餐食名称，纵轴上标注频数，所使用的刻度至少到达 20。条形之间留有等宽的间隔，因为这些类别并非有序数值。
Bar Chart: Frequency → Height / 条形图：频数 → 高度
To see the proportions more clearly, we also draw a pie chart. The full circle (360°) represents all 80 students. The angle for Fish Fingers is (20 ÷ 80) × 360° = 90°. We calculate each angle and draw sectors with a protractor. This helps the catering manager see that exactly a quarter of students prefer Fish Fingers and another quarter choose Sandwich Platter.
为了更清楚地看到各部分的比例，我们还画了饼图。整个圆（360°）代表全部 80 名学生。炸鱼条对应的角度为 (20÷80)×360°=90°。我们计算每个角度并用量角器画出扇形。这能帮助餐饮经理看到，恰好四分之一的学生偏爱炸鱼条，另有四分之一选择三明治拼盘。
Pie Chart Angle = (Frequency ÷ Total) × 360° / 饼图角度公式
5. Reporting the Canteen Findings – Averages Are Not Always the Answer | 报告食堂调查结果——平均数并非总是答案
You might think we should calculate the mean. But this is categorical data, so the mean makes no sense – you cannot have an ‘average meal deal’. The mode (most frequent category) is the sensible summary here. The mode is bimodal: Fish Fingers and Sandwich Platter both appear 20 times. We report this clearly and suggest the canteen should stock more of these two items.
你可能会想，我们应该计算平均数。但这是分类数据，计算平均数毫无意义——你不可能有一个“平均套餐”。这里的合理总结量是众数（出现最频繁的类别）。本例中的众数是双峰的：炸鱼条和三明治拼盘各出现 20 次。我们清楚地报告这一点，并建议食堂多备这两种餐食。
We also calculate the range of frequencies: highest (20) minus lowest (12) equals 8. This tells us there is a moderate spread in popularity, but no meal deal is overwhelmingly ignored. Next we write a short conclusion using the PPDAC cycle: Problem (what to stock), Plan (survey), Data (tally chart), Analysis (bar chart, mode), Conclusion (stock Fish Fingers and Sandwich Platter more).
我们还计算了频数的极差：最高（20）减去最低（12）等于 8。这告诉我们受欢迎程度的分布有一定差距，但没有哪种套餐被普遍冷落。接下来，我们利用 PPDAC 循环撰写简短结论：问题（备餐需求）、计划（问卷调查）、数据（划记表）、分析（条形图、众数）、结论（多备炸鱼条和三明治拼盘）。
6. Case Study 2 – Weather Watch: Daily Maximum Temperatures | 案例研究二——天气观察：每日最高气温
For our second case study we turn to numerical continuous data. A Year 8 class records the daily maximum temperature (in °C) at noon for 20 consecutive school days in March. The aim is to spot patterns and decide if it is warm enough for outdoor PE without jackets.
在第二个案例研究中，我们转向数值连续数据。一个八年级班级连续记录了三月 20 个上学日的中午最高气温（单位：°C）。目标是发现规律，并判断是否足够暖和，可以不用穿外套上户外体育课。
Data set: 9, 11, 10, 8, 12, 14, 13, 10, 11, 9, 15, 16, 14, 13, 12, 10, 11, 14, 15, 13
7. Organising the Temperature Data – Ordered List and Stem‑and‑Leaf Plot | 整理气温数据——有序列表与茎叶图
We begin by sorting the data from smallest to largest. A quick scan shows the minimum is 8°C and the maximum is 16°C. The ordered list helps, but a stem‑and‑leaf diagram is even better because it preserves every value while showing shape. We use the tens digit as the stem and the units digit as leaves. For these data, stems are 0 (for 8 and 9) and 1 (for 10–16).
我们首先将数据从小到大排序。快速扫视后可知最小值为 8°C，最大值为 16°C。有序列表固然有用，但茎叶图更佳，因为它保留了每一个数据值，同时还能显示分布形状。我们使用十位数作茎，个位数作叶。这个数据集的茎为 0（对于 8 和 9）和 1（对于 10 到 16）。
Stem‑and‑leaf / 茎叶图:
0 | 8 9
1 | 0 0 0 1 1 1 2 2 3 3 3 4 4 4 5 5 6
Key: 1 | 2 means 12°C / 图例：1 | 2 表示 12°C
The diagram makes it easy to see the mode (10°C and 14°C both appear three times) and the shape – temperatures are fairly spread out but clustered between 10°C and 15°C. No stem is missing, so there is not a large gap in the data.
该图让人一目了然地看到众数（10°C 和 14°C 各出现三次）和分布形状——气温较为分散，但主要集中在 10°C 到 15°C 之间。没有缺茎，说明数据中没有明显的巨大缺口。
8. Calculating Averages and Range – Summarising the Weather | 计算平均值与极差——总结天气情况
Temperature data is numerical, so the mean is meaningful. We add all 20 temperatures to get a total of 240°C and then divide by 20 to obtain a mean of 12°C. The median is the middle value of the ordered list. With 20 values, the median lies between the 10th and 11th values: (12 + 12) ÷ 2 = 12°C. The mode from the stem‑and‑leaf plot is 10°C and 14°C (bimodal). The range is maximum – minimum = 16 – 8 = 8°C. This tells us that temperatures varied by 8 degrees over the month.
气温数据属于数值型，因此计算平均值是有意义的。我们将 20 个气温加起来，总和为 240°C，再除以 20，得出平均值为 12°C。中位数是有序列表的中间值。共有 20 个数值，中位数位于第 10 和第 11 个值之间：(12+12)÷2=12°C。从茎叶图读取众数，为 10°C 和 14°C（双峰）。极差为最大值减最小值：16−8=8°C。这告诉我们，本月气温波动幅度为 8 度。
Because the mean and median are both 12°C, the distribution is roughly symmetric. If the mean had been much higher than the median, it would suggest a few unusually warm days pulling the average up.
由于平均数和中位数都是 12°C，分布大致对称。如果平均数远高于中位数，就说明有少数异常暖和的日子拉高了平均值。
9. Choosing the Right Graph – Time‑Series and Line Graphs | 选择正确的图表——时间序列与折线图
Since temperature was recorded over time, a line graph (or time‑series plot) is the clearest way to display it. We plot each day’s temperature along a horizontal time axis and join the points with segments. This reveals a gentle upward trend from day 1 to day 20, suggesting that March was getting warmer. We also add a horizontal line at the mean (12°C) to see how many days stayed above average.
由于气温是按时间顺序记录的，折线图（或时间序列图）是最清晰的展示方式。我们在横轴（时间轴）上标出每一天的气温，并将各点用线段连接。图形显示从第 1 天到第 20 天呈现缓慢上升的趋势，表明三月正在变暖。我们还在平均数（12°C）处添加了一条水平线，以观察有多少天的气温高于平均水平。
Time on horizontal axis, Temperature on vertical axis / 横轴为时间，纵轴为气温
The line graph helps the PE teacher make a decision: by the end of the observed days, temperatures were consistently 14°C or above, so outdoor PE without jackets seems sensible from day 16 onwards.
折线图帮助体育老师做了决定：在观测期的末尾，气温持续在 14°C 或以上，因此从第 16 天开始，无需穿外套上户外体育课是合理的。
10. Case Study 3 – Book Shop Survey: Comparing Two Samples | 案例研究三——书店调查：比较两组样本
Our final challenge is a comparative investigation. A local bookshop runs two Young Reader clubs: Club A (ages 10–11) and Club B (ages 12–13). The manager wants to know the typical number of books read in a month and whether there is a real difference between the two age groups. Each club surveys 15 of its members.
我们最后的挑战是一项比较性调查。当地一家书店设有两个小读者俱乐部：俱乐部 A（10–11 岁）和俱乐部 B（12–13 岁）。经理想知道每月读书数量的典型情况，以及两个年龄组之间是否存在真实差异。每个俱乐部各调查了 15 名成员。
Club A (books read): 3, 4, 2, 5, 4, 3, 6, 2, 4, 5, 3, 4, 6, 4, 5
Club B (books read): 5, 7, 6, 8, 5, 9, 7, 6, 8, 7, 5, 6, 9, 8, 7
11. Comparing with Dual Stem‑and‑Leaf Plots | 使用背靠背茎叶图进行比较
To compare distributions directly, we construct a back‑to‑back stem‑and‑leaf diagram. The stem represents the whole number of books. Leaves for Club A extend to the left of the stem, and leaves for Club B to the right. This compact display shows shape, centre and spread for both groups simultaneously.
为了直接比较分布，我们制作了背靠背茎叶图。茎代表书本数量的整数部分。俱乐部 A 的叶向左延伸，俱乐部 B 的叶向右延伸。这种紧凑的展示能同时显示出两组的形状、中心和离散程度。
Club A ← | Stem | → Club B
2 2 | 2 |
3 3 3 | 3 |
4 4 4 4 4 | 4 |
5 5 5 | 5 | 5 5 5
6 6 | 6 | 6 6 6
| 7 | 7 7 7 7
| 8 | 8 8 8
| 9 | 9 9
Key: 4 | 5 means 5 books for Club A; 5 | 7 means 7 books for Club B.
图例：4 | 5 表示 A 部读 5 本；5 | 7 表示 B 部读 7 本。
The diagram reveals that Club B’s distribution is shifted towards higher numbers, with a noticeable gap around 4 books. Club A is more concentrated around 4 books, while Club B is centred around 7 books.
该图揭示出 B 部的分布向较高数值平移，在 4 本附近有一个明显缺口。A 部集中在 4 本左右，而 B 部的中心在 7 本左右。
12. Comparing Centers and Spreads – Mean, Median and Range | 比较中心与离散程度——平均数、中位数和极差
We now compute summaries for each group. For Club A, the total books read is 60, giving a mean of 60 ÷ 15 = 4 books. The ordered list gives a median of 4 books (the 8th value). The range is 6 – 2 = 4 books. For Club B, the total is 103, mean = 103 ÷ 15 ≈ 6.87 (round to 6.9 books). The median is the 8th value: 7 books. Range = 9 – 5 = 4 books.
我们现在为每个组计算概括统计量。A 部的总阅读数为 60 本，平均值 = 60÷15=4 本。有序列表的中位数为 4 本（第 8 个值）。极差 = 6−2=4 本。B 部的总阅读数为 103 本，平均值 = 103÷15≈6.87（四舍五入为 6.9 本）。中位数为第 8 个值：7 本。极差 = 9−5=4 本。
| Measure | Club A | Club B |
|---|---|---|
| Mean (books) | 4 | 6.9 |
| Median (books) | 4 | 7 |
| Range (books) | 4 | 4 |
Both groups show the same range of 4 books, telling us the variation in reading habits is similar. However, the mean and median for Club B are about 3 books higher. This supports the visual message of the stem‑and‑leaf plot: older club members tend to read more books per month. We must also note that Club B’s mean is slightly lower than its median (6.9 vs 7), which suggests a slight left‑skew – a couple of lower values pull the mean down a little.
两组的极差都是 4 本，说明阅读习惯的变异程度相似。然而，B 部的平均数和中位数都高出约 3 本。这验证了茎叶图的直观信息：年长会员每月通常会读更多的书。我们还注意到 B 部的平均数略低于中位数（6.9 对比 7），暗示分布略微左偏——个别较低的值将平均数轻微拉低。
13. CCEA-Style Reflective Questions – Thinking Like an Examiner | CCEA 风格反思题——像考官一样思考
To deepen understanding, practise answering questions like these: Why did we not use a pie chart for the temperature data? (Because temperature is continuous over time, a line graph shows trend better.) Why might the book survey have response bias? (Pupils who read a lot may be prouder to respond; those who read little might not answer truthfully.) How could the canteen survey be improved? (Ask on multiple days, include Year 9 and 10, offer a free‑text option.)
为了加深理解，练习回答以下问题：为什么我们对气温数据不选用饼图？（因为气温是随时间变化的连续数据，折线图更能展示趋势。）为什么图书调查可能存在回答偏差？（阅读量大的学生可能更愿意骄傲地作答；阅读量少的或许不会如实回答。）如何改进食堂调查？（在多个日子询问、纳入九年级和十年级、增设自由填写选项。）
Each time you answer such a question, you are reinforcing the most valuable statistical habit: not just calculating, but asking ‘what does this number really tell me?’ and ‘could the data be misleading?’. That is what CCEA examiners look for in high‑band answers.
每当你回答这类问题，你都在强化最有价值的统计习惯：不仅仅是计算，而是追问“这个数字真正告诉我什么？”以及“数据会误导我吗？”。这正是 CCEA 考官在优秀答案中所寻找的。
14. Your Turn – Mini Investigation Design | 轮到你了——微型调查设计
Now plan your own mini case study. Choose a simple question from your daily life: How many minutes do classmates spend on homework? What is the most common eye colour in your year group? What is the range of shoe sizes? Write the aim, collect at least 15 data points, draw a stem‑and‑leaf plot or bar chart, calculate the mean, median, mode and range, and write a one‑paragraph conclusion. Focus on clear presentation and honest interpretation – even if the results surprise you.
现在来规划你自己的微型案例研究。从日常生活中选一个简单问题：同学花在作业上的时间是多少分钟？你年级中最常见的眼睛颜色是什么？鞋码的极差是多少？写出目标，收集至少 15 个数据点，画出茎叶图或条形图，计算平均数、中位数、众数和极差，并撰写一段结论。专注于清晰的呈现和诚实的解读——即使结果让你感到意外。
Remember, in CCEA Statistics, a ‘wrong’ answer supported by clear reasoning is often worth more marks than a correct answer with no explanation. Show every step and explain what each calculation reveals.
请记住，在 CCEA 统计学中，一个有清晰推理支撑的“错误”答案，常常比一个没有解释的正确答案得分更高。要展示每一步，并解释每一项计算所揭示的信息。
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