📚 KS3 Edexcel Statistics: Case Study Practice | KS3 Edexcel 统计：案例分析实战演练
In this article, we will work through a complete statistical investigation from start to finish, just as you would in a KS3 Edexcel statistics project. You will follow a real-world scenario – a survey on students’ weekly screen time – and practise every key skill: designing a questionnaire, collecting and organising data, drawing charts, calculating averages and range, estimating probability, and writing conclusions. By the end, you will feel confident in applying statistical methods to any case study you meet in tests or coursework.
本文将通过一个完整的统计调查案例，带你走完从计划到结论的全过程，就像你在 KS3 Edexcel 统计项目中所做的那样。我们将以学生每周屏幕时间调查为真实情境，逐一练习问卷设计、数据收集整理、绘制图表、计算平均数与极差、估计概率以及撰写结论等核心技能。读完这篇文章，你就能自信地将统计方法应用到考试或作业中的任何案例分析题上。
1. Setting the Scene: The Screen Time Investigation | 设定场景：屏幕时间调查
Imagine you are a Year 9 student who wants to find out how many hours your classmates spend looking at screens each week. This is an interesting question because too much screen time can affect sleep and concentration. To answer it properly, you need to plan a statistical enquiry. You decide to ask: 'How many hours in total do you spend on phones, tablets, computers and TV in a typical week?'
假设你是一名九年级学生，想了解同班同学每周花在屏幕上的时间有多少。这个问题很有趣，因为过长的屏幕时间可能影响睡眠和注意力。为了很好地回答它，你需要设计一项统计调查。你决定提问：“在一周内，你通常花在手机、平板、电脑和电视上的总时间是多少小时？”
Before you rush off to ask everyone, think about the population and the sample. Your population is all students in your school, but surveying hundreds of pupils would take too long. You therefore choose a sample of 30 students from your year group. A good sample should be representative, so you decide to select students randomly from the register. This makes your investigation both manageable and fair.
在急着去问每个人之前，先想一想总体和样本。你的总体是学校里的全体学生，但调查几百人会花费太多时间。因此，你从所在年级中选取了 30 名学生作为样本。一个好的样本应当具有代表性，所以你决定从班级名单中随机抽取学生。这使调查既便于操作又公正科学。
2. Designing the Questionnaire | 设计问卷
Your questionnaire needs just one main question, but it must be clear and easy to answer. You write: 'In a typical week, approximately how many hours do you spend on screen-based activities (phone, tablet, gaming, TV, computer)? Please round your answer to the nearest whole hour.' You also include a short introduction explaining why you are collecting data and promise that answers are anonymous.
你的问卷只需要一个主要问题，但一定要清晰易答。你写道：“在一周内，你花在屏幕类活动（手机、平板、游戏、电视、电脑）上的时间大约有多少小时？请将答案四舍五入到最近的整小时。”你还加了一段简短说明，解释收集数据的目的，并承诺所有回答都将匿名处理。
You test your question on two friends first. One says 15 hours, the other says 24. Both understood it immediately, so you are ready to collect the real data. This pilot test helps you check that the question wording does not confuse people and that the data type is suitable – in this case discrete numerical data.
你先让两位朋友试答问题。一位回答 15 小时，另一位回答 24。两人都立刻理解了问题，说明你可以正式开始收集数据了。这种小范围测试能帮你检查问题表述是否会造成混淆，并确认数据类型合适——在这个案例中是离散型数值数据。
3. Collecting the Data | 收集数据
With a printed questionnaire and a clipboard, you approach your 30 randomly selected participants during break time. You record their answers carefully. Here is the raw data set you collect (number of hours per week): 12, 18, 14, 10, 22, 8, 15, 20, 17, 13, 25, 9, 19, 16, 11, 28, 21, 14, 7, 23, 18, 30, 12, 16, 10, 27, 13, 15, 19, 24.
你拿着打印好的问卷和写字板，在课间休息时找到了随机抽取的 30 位参与者，并仔细记录下他们的回答。以下是你收集到的原始数据（每周小时数）：12, 18, 14, 10, 22, 8, 15, 20, 17, 13, 25, 9, 19, 16, 11, 28, 21, 14, 7, 23, 18, 30, 12, 16, 10, 27, 13, 15, 19, 24。
Seeing a long list of numbers is confusing, so your next job is to organise them. You notice the smallest value is 7 hours and the largest is 30 hours. The range is already interesting – that shows a big difference in screen habits! But before you jump to conclusions, you need a frequency table to see patterns more clearly.
看到这么一长串数字很容易让人眼花，因此下一步就是整理数据。你发现最小值是 7 小时，最大值是 30 小时。极差这么大已经很有意思了，它反映出屏幕习惯的巨大差异！不过在下结论之前，你需要制作一张频数表，以便更清楚地看出分布规律。
4. Organising Data: Frequency Table | 整理数据：频数表
To group the data, you create equal class intervals. Since the values range from 7 to 30, you might use intervals of width 4 hours: 7–10, 11–14, 15–18, 19–22, 23–26, 27–30. Then you count how many students fall into each interval. This is called a grouped frequency table. Remember to make sure the intervals do not overlap and that every piece of data fits into exactly one group.
为了将数据分组，你需要设置等宽的组距。由于数据从 7 到 30，可以选择组距为 4 小时：7–10、11–14、15–18、19–22、23–26、27–30。然后数出每个区间内的学生人数，这就得到了分组频数表。注意要确保组距不重叠，且每条数据都能恰好归入一个组。
| Screen time (hours) | Tally | Frequency |
|---|---|---|
| 7 – 10 | |||| | 4 |
| 11 – 14 | |||| || | 7 |
| 15 – 18 | |||| |||| | 9 |
| 19 – 22 | |||| | | 6 |
| 23 – 26 | ||| | 3 |
| 27 – 30 | | | 1 |
From the frequency table, you can see that the modal class is 15–18 hours, with 9 students. Very few students are in the highest interval, which is also known as the 'tail' of the distribution. Tables like this make it much easier to spot the shape of the data and prepare for drawing charts.
从频数表可以看出，众数所在组是 15–18 小时，有 9 名学生。最高区间内的学生非常少，这通常被称为分布的“尾部”。像这样的表格能让你更容易发现数据的分布形状，也为绘制图表做好了准备。
5. Visualising Data: Bar Chart and Pie Chart | 数据可视化：条形图与饼图
Now you can present your data visually. A bar chart is perfect for showing the frequencies of different groups. You plot the intervals on the horizontal axis and the frequencies on the vertical axis. Each bar’s height represents the number of students in that interval. Bars should be of equal width and should touch, as the data is continuous when grouped.
现在你可以用图表直观地展示数据了。条形图非常适合显示不同组别的频数。你把组距放在横轴，频数放在纵轴，每个条形的高度代表该组的学生人数。条形的宽度应当相等，并且因为分组数据是连续的，条形之间应紧挨在一起。
ie chart to show the proportion of students in each category. To find the angle for the 15– l intervals gives a clear picture of the relative sizes. However, a bar chart is often better when comparing exact frequencies, while a pie chart is good for emphasising proportions.
你还可以绘制饼图来展示每个类别的比例。要计算 15–18 小时扇区的角度，可用公式：(9 ÷ 30) × 360° = 108°。对所有组重复此计算，就能得到各扇区大小。条形图更适合比较精确的频数，而饼图则擅长强调整体中的占比。
In your report, you include both charts with clear labels and a title. This helps readers quickly grasp the key message: most students spend between 11 and 22 hours on screens per week, and very few exceed 26 hours. Visuals are powerful tools in any statistical case study.
在你的报告中，你放上了两张带有清晰标签和标题的图表。这能帮助读者迅速抓住关键信息：大多数学生每周花在屏幕上的时间在 11 到 22 小时之间，很少会超过 26 小时。在任何统计案例分析中，图表都是非常有力的表达工具。
6. Calculating the Mean | 计算平均数
a grouped frequency table, you first need to estimate the midpoint of each interval. For 7–10, the midpoint is (7+10)÷2 = 8.5. For 11– its frequency, sum all those products, and divide by the total frequency. The formula is:
要从分组频数表计算算术平均数，首先需要估算每个组的中点值。7–10 的中点为 (7+10)÷2 = 8.5，11–14 的中点为 12.5，以此类推。然后用每个中点数乘以对应的频数，将所有这些乘积相加，再除以总频数。公式为：
Mean ≈ (Σ f × midpoint) ÷ Σ f
平均数 ≈ (Σ f × 中点值) ÷ Σ f
of students is 30, so the estimated mean is 495 ÷ 30 = 16.5 hours. This tells you that the 'typical' student spends about 16.5 hours a week on screens.
代入我们的表格：（4×8.5）+（7×12.5）+（9×16.5）+（6×20.5）+（3×24.5）+（1×28.5）= 34 + 87.5 + 148.5 + 123 + 73.5 + 28.5 = 495。总人数为 30，因此估算的平均数为 495 ÷ 30 = 16.5 小时。这表明“典型”学生每周大约花 16.5 小时在屏幕上。
7. Median and Mode from Raw Data | 从原始数据求中位数与众数
You can also find the median and mode using the raw, ungrouped list. First, sort the 30 values from smallest to largest: 7, 8, 9, 10, 10, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 18, 18, 19, 19, 20, 21, 22, 23, 24, 25, 27, 28, 30. The median is the middle value. Because there are 30 numbers, the median lies between the 15th and 16th values. Both are 16, so the median is 16 hours.
你也可以用未分组的原始数据来求中位数和众数。首先，将 30 个数值从小到大排序：7, 8, 9, 10, 10, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 18, 18, 19, 19, 20, 21, 22, 23, 24, 25, 27, 28, 30。中位数是中间的值。因为有 30 个数字，中位数位于第 15 和第 16 个值之间，这两个值都是 16，因此中位数为 16 小时。
The mode is the value that appears most often. By scanning the list, you see that 10, 12, 13, 14, 15, 16, 18, and 19 each appear twice. So this data set is multimodal. In cases like this, the mode is less useful for describing a 'typical' value, but it does tell you that several screen-time amounts are equally common. The mean and median together give a better summary.
众数是出现次数最多的值。浏览排序表可以发现，10、12、13、14、15、16、18 和 19 都分别出现了两次，所以这个数据集是多众数的。在这种情况下，众数不太适合用来描述“典型”值，但它说明了好几种屏幕时间长短都同样常见。把平均数和中位数结合起来能给出更好的概括。
8. Measuring Spread: Range and Identifying Outliers | 度量离散程度：极差与识别异常值
The range is the simplest measure of spread. From your raw data, the maximum screen time is 30 hours and the minimum is 7 hours.
极差是反映数据离散程度最简单的指标。从你的原始数据来看，最大屏幕时间是 30 小时，最小是 7 小时。
Range = 30 − 7 = 23 hours
极差 = 30 − 7 = 23 小时
A large range of 23 hours confirms that there is considerable variation in screen habits. You might suspect the value 30 is an outlier. To check informally, you can calculate the interquartile range or simply see if it is much larger than the rest. The next highest value is 28, so 30 is not dramatically isolated, but it is still at the extreme end. In a KS3 investigation, it is good practice to comment on any unusual values and consider whether they should be included.
23 小时的较大极差证实了屏幕习惯差异很大。你可能会怀疑 30 是一个异常值。为了进行非正式检验，可以计算四分位距，或简单地观察它是否远大于其他数值。次高值是 28，因此 30 并非突兀地孤立，但仍处于极端位置。在 KS3 的调查中，比较规范的做法是对任何异常值加以评论，并考虑是否应将其纳入分析。
9. Estimating Probability from Data | 从数据估计概率
You can use your frequency table to estimate the probability that a randomly chosen Year 9 student spends more than 22 hours on screens per week. From the table, the intervals that satisfy this are 23–26 (3 students) and 27–30 (1 student). So 4 out of 30 students are in this category. Therefore,
你可以利用频数表来估计，随机选择一名九年级学生每周屏幕时间超过 22 小时的概率。从表中看，满足条件的区间是 23–26（3 人）和 27–30（1 人），因此共有 4 名学生属于这类。
Estimated probability = 4/30 = 2/15 ≈ 0.133
估计概率 = 4/30 = 2/15 ≈ 0.133
This means there is roughly a 13.3% chance that a student picked at random from your sample spends more than 22 hours. Of course, this probability is based on a small sample, so it might change if you surveyed more people. Treating relative frequency as an estimate of probability is a key concept in KS3 statistics.
这意味着，从你的样本中随机抽取一名学生，其屏幕时间超过 22 小时的概率大约为 13.3%。当然，这一概率是基于一个小样本得出的，若调查更多人，结果可能会发生变化。将相对频数视为概率的估计值是 KS3 统计中的一个重要概念。
10. Drawing Conclusions and Evaluating the Investigation | 得出结论并评估调查过程
Your statistical investigation has revealed several things: the average screen time for Year 9 students is around 16–17 hours per week, but the variation is wide. The distribution is slightly skewed to the right, with a tail of very high users. You conclude that while many students have moderate screen habits, a minority spend noticeably more time, which might be worth investigating further in relation to sleep or academic performance.
你的统计调查揭示了以下几点：九年级学生平均每周屏幕时间约为 16–17 小时，但离散程度很大。分布略微右偏，存在一小部分极高使用者的长尾。你可以得出结论：虽然很多学生屏幕使用处于中等水平，但少数学生花费的时间明显更多，这或许值得结合睡眠或学业表现进一步研究。
Every good case study ends with an evaluation. You reflect on what went well: the questionnaire was easy to understand, the random sample reduced bias, and the range of graphs helped communicate results. However, there are limitations: the sample size was only 30, the data relied on students’ memory and honesty, and the grouping of intervals might hide interesting details. You also suggest improvements, such as asking for screen time on weekdays versus weekends separately, or recording data over a diary for one week for greater accuracy.
每一个优秀案例分析都要以评估收尾。你回顾了做得好的地方：问卷通俗易懂，随机样本降低了偏差，多种图表有助于传达结果。但也有一些局限性：样本容量仅为 30，数据依赖于学生的记忆和诚实度，而分组可能掩盖了某些有趣的细节。你还提出了改进建议，例如分别询问平日和周末的屏幕时间，或让学生记录一周的日记以获得更准确的数据。
Published by TutorHao | KS3 Statistics Revision Series | aleveler.com
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