📚 Year 7 CCEA Statistics: Case Study Drill | CCEA 七年级统计：案例分析实战演练
Statistics becomes much easier to understand when you work through a complete example from start to finish. In this case study, you will follow the journey of a real data investigation: collecting raw information, organising it into tables and charts, calculating summary measures, and finally drawing sensible conclusions. By the end, you will have practised every key skill from the Year 7 CCEA statistics syllabus in one engaging drill.
当你从头到尾完成一个完整的实例时，统计学会变得容易理解得多。在本案例研究中，你将跟随一项真实的数据调查之旅：收集原始信息，将其整理为表格和图表，计算汇总度量，最后得出合理的结论。到结束时，你将在一次引人入胜的演练中练习七年级CCEA统计课程中的每一项关键技能。
1. Understanding the Scenario | 理解场景
A school wants to find out how Year 7 pupils travel to school each morning. The teacher asks one class of 24 students to record their main method of transport for a week. The possible answers are Walk, Bicycle, Bus, and Car. By analysing this data, the school can plan better facilities, such as bike sheds or a safe walking route.
一所学校想了解七年级学生每天早上如何上学。老师让一个有 24 名学生的班级记录他们一周的主要交通方式。可能的答案有步行、自行车、公共汽车和小汽车。通过分析这些数据，学校可以规划更好的设施，例如自行车棚或安全的步行路线。
2. Raw Data Collection | 原始数据收集
The raw list of 24 responses looks like this: Walk, Bus, Car, Walk, Bicycle, Bus, Bus, Car, Walk, Bus, Car, Walk, Bicycle, Bus, Walk, Bus, Car, Bicycle, Walk, Bus, Car, Bus, Bicycle, Car. Notice that the data is just a jumble of words – it is very hard to spot any patterns at this stage.
24 条原始回答列表如下：步行、公共汽车、小汽车、步行、自行车、公共汽车、公共汽车、小汽车、步行、公共汽车、小汽车、步行、自行车、公共汽车、步行、公共汽车、小汽车、自行车、步行、公共汽车、小汽车、公共汽车、自行车、小汽车。请注意，这些数据只是一堆杂乱的词汇——在这个阶段很难发现任何规律。
3. Tallying and Frequency Table | 画正字与频数表
To bring order, we use tally marks. Each time a transport type appears, we draw a tally. When we reach the fifth tally, we draw a diagonal line through the first four to make a group of five. Then we count the tallies to find the frequency – the number of students using each method.
为了理清顺序，我们使用画正字的方法。每当一种交通方式出现时，我们就画一笔计数。数到第五笔时，我们在前四笔上画一条斜线，形成一组五笔。然后我们数出正字的数量，得出频数——即使用每种方式的学生人数。
| Mode of Transport | Tally | Frequency |
|---|---|---|
| Walk | IIII I | 6 |
| Bicycle | IIII | 4 |
| Bus | IIII III | 8 |
| Car | IIII I | 6 |
Always check your total frequency. Here 6 + 4 + 8 + 6 = 24, which matches the number of students, so the table is correct.
一定要检查总频数。这里 6 + 4 + 8 + 6 = 24，与学生人数相符，因此表格是正确的。
4. Creating a Bar Chart | 创建条形图
A bar chart is a great way to display categorical data. The categories go along the horizontal axis, and the frequency goes up the vertical axis. The bars must be of equal width, with gaps between them to show that the categories are separate. For our data, the bar for Bus would rise to 8, Walk and Car both reach 6, and Bicycle would be the shortest at 4.
条形图是展示分类数据的好方法。类别放在横轴上，频数放在纵轴上。条形必须宽度相等，且条形之间要有间隙，以表明类别是独立的。对于我们的数据，公共汽车的条形将上升到 8，步行和小汽车都达到 6，自行车最短，为 4。
When drawing by hand, use a ruler and sharp pencil. Label the axes clearly: ‘Mode of Transport’ on the x-axis and ‘Frequency’ on the y-axis. Give the chart a title such as ‘How Year 7 Students Travel to School’.
手工绘制时，请使用直尺和尖细的铅笔。清楚地给坐标轴添加标签：横轴标为“交通方式”，纵轴标为“频数”。给图表加上标题，例如“七年级学生上学方式”。
5. Reading Bar Charts | 阅读条形图
Once the chart is drawn, you can read it almost instantly. The tallest bar represents the mode – the most common category. Here Bus is clearly the most popular. You can also compare bars: about twice as many students take the bus as ride a bicycle. This visual comparison is one of the main reasons bar charts are so widely used.
图表绘制完成后，你几乎可以立即读懂它。最高的条形代表众数——最常见的类别。这里公共汽车显然是最受欢迎的。你还可以比较条形的高度：乘公共汽车的学生人数大约是骑自行车学生的两倍。这种视觉对比是条形图被如此广泛使用的主要原因之一。
Never forget that the chart must have a key or clear labels if colours are used. However, for a simple bar chart like this, colour is optional; the height alone tells the story.
千万不要忘记，如果使用了颜色，图表必须配有图例或清晰的标签。不过，对于这样的简单条形图，颜色是可选的；仅凭高度就能说明问题。
6. The Mode: Most Popular Transport | 众数：最受欢迎的出行方式
The mode is the value that appears most often in a data set. From our frequency table, Bus has the highest frequency of 8. So we say the mode is ‘Bus’. The mode is especially useful for categorical data because it tells us the typical category without needing to do any number crunching.
众数是数据集中出现频率最高的值。从我们的频数表中可以看出，公共汽车的频数最高，为 8。因此我们说众数是“公共汽车”。众数对于分类数据特别有用，因为它无需进行数字运算就能告诉我们最典型的类别。
If two categories had the same highest frequency, the data would be bimodal – having two modes. Here we have a single mode, which makes the summary very clean.
如果两个类别具有相同的最高频数，那么数据就是双众数的——拥有两个众数。这里我们只有一个众数，这使得总结非常简洁。
7. Why the Median Doesn’t Fit Here | 为什么这里不适合用中位数
You might have learned that the median is the middle value when data is ordered. However, ‘Walk’, ‘Bus’, and ‘Car’ do not have a natural order – they are just names. Trying to sort them alphabetically and pick the middle one would give a misleading answer, because the order ‘Bicycle, Bus, Car, Walk’ is arbitrary and does not tell you which transport sits in the centre of the data in a meaningful way.
你可能学过，中位数是将数据排序后位于中间的值。然而，“步行”“公共汽车”和“小汽车”并没有自然的顺序——它们只是名称罢了。如果尝试按字母顺序排列并挑选中间的，就会得到一个误导性的答案，因为“自行车、公共汽车、小汽车、步行”的顺序是任意的，并不能以有意义的方式告诉你哪一种交通方式处于数据的中心。
This is a key rule: the median only makes sense for data that can be ordered, such as numbers or ranks like ‘Strongly agree, Agree, Neutral, Disagree, Strongly disagree’. For our case study, we stick with the mode.
这是一条关键规则：中位数只对可以排序的数据有意义，比如数字或诸如“非常同意、同意、中立、不同意、非常不同意”这样的等级。在我们的案例研究中，我们坚持使用众数。
8. Constructing a Pie Chart | 构建饼图
A pie chart shows proportions of a whole. The entire circle represents all 24 students. To find the angle for each sector, we use the formula:
Angle = (Frequency ÷ Total) × 360°
饼图展示的是整体的各部分比例。整个圆代表全部 24 名学生。要计算每个扇区的角度，我们使用以下公式：
角度 = (频数 ÷ 总数) × 360°
For Walk: (6 ÷ 24) × 360° = 90°. For Bicycle: (4 ÷ 24) × 360° = 60°. For Bus: (8 ÷ 24) × 360° = 120°. For Car: (6 ÷ 24) × 360° = 90°. Always check that the angles sum to 360°: 90 + 60 + 120 + 90 = 360.
步行：(6 ÷ 24) × 360° = 90°。自行车：(4 ÷ 24) × 360° = 60°。公共汽车：(8 ÷ 24) × 360° = 120°。小汽车：(6 ÷ 24) × 360° = 90°。一定要检查角度总和是否为 360°：90 + 60 + 120 + 90 = 360。
When drawing, use a protractor to measure each angle accurately from the centre. Label each sector with the transport name and either the frequency or the percentage. This helps the reader see instantly that Bus takes up one third of the circle.
绘图时，使用量角器从圆心准确地量出每个角度。在每个扇区上标出交通方式的名称以及频数或百分比。这有助于读者一眼就看出公共汽车占据了圆的三分之一。
9. Using Percentages | 使用百分比
Percentages make it easy to compare parts of a whole, especially when the total is not a round number like 100. To calculate the percentage for each transport, use:
Percentage = (Frequency ÷ Total) × 100%
百分比能让你轻松比较整体的各个部分，尤其是在总数不是像 100 这样的整数时。要计算每种交通方式的百分比，请使用：
百分比 = (频数 ÷ 总数) × 100%
For Walk: (6 ÷ 24) × 100% = 25%. Bicycle: (4 ÷ 24) × 100% ≈ 16.7%. Bus: (8 ÷ 24) × 100% ≈ 33.3%. Car: (6 ÷ 24) × 100% = 25%. You can round percentages to one decimal place and note that they still sum to 100%.
步行：(6 ÷ 24) × 100% = 25%。自行车：(4 ÷ 24) × 100% ≈ 16.7%。公共汽车：(8 ÷ 24) × 100% ≈ 33.3%。小汽车：(6 ÷ 24) × 100% = 25%。你可以将百分比四舍五入到一位小数，并注意它们的总和仍为 100%。
Adding percentages to a pie chart or a frequency table gives the school extra insight – for example, that one in four students walks and one in four comes by car, while roughly one in three uses the bus.
将百分比添加到饼图或频数表中，会给学校带来额外的洞察——例如，四分之一的学生步行，四分之一乘小汽车，而大约三分之一乘公共汽车。
10. Writing a Summary | 撰写总结
Once all the calculations and charts are complete, it is time to write a short summary. A good summary states the context, the main finding, and possibly a suggestion. For this case study, you could write: ‘In a survey of 24 Year 7 students, the most common way to travel to school was by bus (8 students, 33.3%). Walking and car were equally common at 6 students each, while cycling was the least popular with only 4 students.’
当所有的计算和图表都完成后，就该撰写一个简短的总结了。一个好的总结要陈述背景、主要发现，可能的话还要提出建议。对于这个案例研究，你可以这样写：“在一项对 24 名七年级学生的调查中，最常见的上学方式是乘公共汽车（8 名学生，占 33.3%）。步行和乘小汽车同为 6 人，同样普遍，而骑自行车最不受欢迎，只有 4 人。”
A suggestion might follow: ‘To encourage more cycling, the school could install secure bike racks and offer a cycling proficiency course.’ This turns the data into action – exactly what statistics is meant to do.
接下来可以提一条建议：“为了鼓励更多人骑自行车，学校可以安装安全的自行车停放架，并开设自行车技能课程。”这样就把数据转化为了行动——这正是统计学的意义所在。
11. Comparing Two Groups (Extension) | 比较两组数据（拓展）
What if the school also surveyed a Year 8 class and found the frequencies: Walk 10, Bicycle 7, Bus 5, Car 2? You can compare the two bar charts side by side. The Year 8 data shows a big drop in bus use and a rise in walking and cycling. Percentages help here too: Year 8 Bus is only about 20.8% (5 out of 24) compared with 33.3% in Year 7.
如果学校还调查了一个八年级班级，得到频数为：步行 10、自行车 7、公共汽车 5、小汽车 2，该怎么办？你可以将两个条形图并排比较。八年级的数据显示乘公共汽车的人数大幅下降，而步行和骑自行车的人数上升。此时百分比也能帮上忙：八年级乘公共汽车的比例仅为约 20.8%（24 人中有 5 人），而七年级为 33.3%。
Drawing dual bar charts or multiple pie charts lets you ask interesting questions: Are older students more independent? Could a safer cycle route increase cycling in all year groups? Group comparisons are a powerful extension of basic statistical skills.
绘制双重条形图或多个饼图，能让你提出有趣的问题：年龄大一些的学生是否更独立？更安全的自行车道能否提高所有年级的骑行比例？分组比较是基础统计技能的一个强有力延伸。
12. Practice Task: Design Your Own Survey | 练习任务：设计你自己的调查
Now it is your turn. Pick a question you can ask your classmates, such as ‘What is your favourite fruit?’ or ‘How do you spend your break time?’ Create a data collection sheet, gather at least 20 responses, and then produce a frequency table, a bar chart, and a short written report. Remember to explain why you chose the mode and whether the median makes sense for your data.
现在轮到你了。选择一个你可以问同学的问题，例如“你最喜欢的水果是什么？”或“你课间休息时做什么？”制作一份数据收集表，收集至少 20 份回答，然后生成频数表、条形图和一份简短的书面报告。记得解释你为什么选择众数，以及中位数对你的数据是否有意义。
This practice task mirrors exactly what you might be asked to do in a CCEA assessment. Keep all your workings neat and labelled, and your final report will show that you truly understand the whole statistical cycle.
这项练习任务完全反映了你可能会在 CCEA 评估中被要求做的事情。保持所有计算步骤整洁并配有标签，你的最终报告将展示出你真正理解了整个统计循环。
Published by TutorHao | Statistics Revision Series | aleveler.com
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