📚 Year 7 SQA Statistics: Case Study Practice | Year 7 SQA 统计：案例分析实战演练
Welcome to our practical case study in statistics, designed for Year 7 students following the SQA curriculum. In this article, we will work through a real‑world scenario where a student investigates the reading habits of their classmates. By collecting, organising, and analysing data, you will see how statistical tools help us understand patterns and make decisions. This hands‑on approach will reinforce your skills in creating frequency tables, drawing charts, calculating averages, and interpreting results – all essential for your SQA assessments.
欢迎来到为 Year 7 SQA 课程设计的统计案例分析实战演练。本文将通过一个真实场景，展示一名学生如何调查同班同学的阅读习惯。通过收集、整理和分析数据，你将看到统计工具如何帮助我们理解模式并做出决策。这种实践方法将巩固你在制作频数表、绘制图表、计算平均数和解读结果方面的技能——这些对于你的 SQA 评估至关重要。
1. Introduction to the Case Study | 案例介绍
Joe, a Year 7 student, wanted to find out how much reading his classmates do outside of school. His statistical question was: “How many pages do my classmates typically read in a week?” This is a clear, measurable question that can be answered using primary data. Joe decided to survey the 20 students in his class and record the number of pages each person read during the previous week.
Joe 是一名 Year 7 学生，他想了解同学们在课外阅读的量。他的统计问题是：“我的同班同学通常每周读多少页书？”这是一个清晰、可测量的问题，可以用一手数据来回答。Joe 决定调查班上的 20 名同学，记录每个人在上周阅读的页数。
The data he collected will be used throughout this case study to demonstrate every step of a statistical investigation: from planning and collecting data, through organising and displaying it, to calculating summary statistics and drawing conclusions.
他收集的数据将贯穿本次案例分析，展示统计调查的每一步：从计划和收集数据，到整理和展示数据，再到计算汇总统计量并得出结论。
2. Data Collection and Recording | 数据收集与记录
Joe designed a simple survey slip asking each classmate: “How many pages did you read for pleasure last week?” He emphasised that answers should be honest and rounded to the nearest whole page. He collected the slips and wrote the raw data in his notebook. The recorded values, in the order they were returned, are shown below.
Joe 设计了一张简单的调查便签，询问每位同学：“上周你为兴趣阅读了多少页？”他强调答案应当诚实，并四舍五入到整页数。他收集便签后将原始数据记录在笔记本上。按照收回顺序，记录的数值如下所示。
Raw data (20 responses): 45, 60, 55, 70, 65, 80, 55, 50, 60, 75, 65, 60, 70, 55, 65, 80, 50, 60, 70, 55
原始数据（20 份回复）：45, 60, 55, 70, 65, 80, 55, 50, 60, 75, 65, 60, 70, 55, 65, 80, 50, 60, 70, 55
Notice that the raw data are unorganised. The numbers jump around, making it difficult to spot any pattern. In statistics, the first important task after collecting data is to organise them so they become easier to understand.
请注意，原始数据是未经整理的。数字来回跳动，很难发现任何模式。在统计学中，收集数据之后的首要任务就是对数据进行整理，使其更易于理解。
3. Organising Data: Frequency Table | 数据整理：频数表
A frequency table helps us see how often each value occurs. Joe listed all the distinct page counts from smallest to largest and then tallied how many students reported each amount. Here is the frequency table he created.
频数表帮助我们看清每个数值出现的次数。Joe 将所有不同的页数从小到大列出，然后统计每个数值有多少名学生报告。下面是他制作的频数表。
| Pages (x) | Tally | Frequency (f) |
|---|---|---|
| 45 | | | 1 |
| 50 | || | 2 |
| 55 | |||| | 4 |
| 60 | |||| | 4 |
| 65 | ||| | 3 |
| 70 | ||| | 3 |
| 75 | | | 1 |
| 80 | || | 2 |
| Total | 20 |
From the table we can immediately see the most common page counts and the spread of values. The total frequency adds up to 20, which matches the number of students surveyed – a useful check.
从表中我们可以立即看出最常见的页数和数值的分布范围。总频数加起来为 20，与被调查的学生人数相符——这是一个有用的核对步骤。
4. Visualising Data: Bar Chart | 数据可视化：条形图
Joe decided to draw a bar chart so that his findings could be shared visually. He put the page counts on the horizontal axis and the frequency on the vertical axis. Each bar height shows the number of students who read that many pages. Because the data are discrete, he left small gaps between the bars.
Joe 决定绘制一张条形图，以便直观地分享他的发现。他将页数放在横轴上，频数放在纵轴上。每个条形的高度表示阅读该页数的学生人数。由于数据是离散的，他在条形之间留出了小间隙。
A bar chart makes it easy to compare frequencies: the bars for 55 and 60 pages are tied as the tallest, each reaching a frequency of 4. The bars for 45 and 75 pages are the shortest, with a frequency of just 1. Plotting data in this way helps the brain spot patterns instantly.
条形图便于比较频数：55 页和 60 页的条形并列最高，频数均为 4。45 页和 75 页的条形最短，频数仅为 1。这种绘图方式有助于大脑快速识别模式。
If you were to sketch this bar chart, you would label the axes clearly, give the chart a title such as “Weekly Reading Pages of Year 7 Students”, and make sure the scale on the frequency axis is evenly spaced.
如果你要绘制这张条形图，你需要清晰地标注坐标轴，给图表加上诸如“Year 7 学生每周阅读页数”的标题，并确保频数轴上的刻度间距均匀。
5. Visualising Data: Pie Chart | 数据可视化：饼图
Another way to display the data is a pie chart, which shows the proportion of students falling into each page‑count category. Joe calculated the angle for each sector using the formula: sector angle = (frequency ÷ total frequency) × 360°.
展示数据的另一种方式是饼图，它显示每个页数类别中学生所占的比例。Joe 使用公式：扇形角度 = (频数 ÷ 总频数) × 360° 计算每个扇形的角度。
For example, the sector for 55 pages has a frequency of 4, so its angle is (4 ÷ 20) × 360° = 72°. The sector for 45 pages, with frequency 1, has an angle of only (1 ÷ 20) × 360° = 18°. Pie charts are excellent for showing how a whole group is divided into parts, although bar charts are often clearer when comparing exact sizes.
例如，55 页的频数为 4，所以其扇形角度为 (4 ÷ 20) × 360° = 72°。45 页的频数为 1，扇形角度仅为 (1 ÷ 20) × 360° = 18°。饼图非常适合展示整体如何被划分为各个部分，不过在比较精确的大小时条形图通常更清晰。
In Joe’s pie chart, the largest slices belong to 55, 60, 65 and 70 pages, together covering more than half of the class. This gives a quick visual impression of where most students’ reading habits lie.
在 Joe 的饼图中，最大的扇形属于 55、60、65 和 70 页，它们合计覆盖了全班一半以上的学生。这能让人快速形成关于多数学生阅读习惯所处范围的直观印象。
6. Measures of Central Tendency: Mean | 集中趋势度量：平均数
The mean is what most people call the “average”. To find the mean number of pages read, we add together all the individual values and then divide by the number of students.
平均数就是大多数人所说的“平均值”。要计算阅读页数的平均数，我们先把所有个别数值加起来，然后除以学生人数。
Mean = (Sum of all pages) ÷ (Number of students)
平均数 = (所有页数之和) ÷ (学生人数)
Using the raw data: 45 + 60 + 55 + 70 + 65 + 80 + 55 + 50 + 60 + 75 + 65 + 60 + 70 + 55 + 65 + 80 + 50 + 60 + 70 + 55 = 1250. There are 20 values, so:
使用原始数据：45 + 60 + 55 + 70 + 65 + 80 + 55 + 50 + 60 + 75 + 65 + 60 + 70 + 55 + 65 + 80 + 50 + 60 + 70 + 55 = 1250。共有 20 个数值，因此：
Mean = 1250 ÷ 20 = 62.5 pages
平均数 = 1250 ÷ 20 = 62.5 页
The mean of 62.5 tells us that if the total pages were shared out equally, each student would read about 62.5 pages per week. Joe can use the mean to compare his class with other groups or to track changes over time.
平均数 62.5 告诉我们，如果把总页数平均分配，每位学生每周大约阅读 62.5 页。Joe 可以用这个平均数与其他班级进行比较，或跟踪随时间的变化。
7. Median and Mode | 中位数和众数
The median is the middle value when the data are written in order from smallest to largest. If there are two middle values, we take their mean. Joe sorted his 20 data values:
中位数是将数据从小到大排序后位于正中间的值。如果有两个中间值，则取它们的平均数。Joe 对他的 20 个数据值进行了排序：
45, 50, 50, 55, 55, 55, 55, 60, 60, 60, 60, 65, 65, 65, 70, 70, 70, 75, 80, 80
With 20 values, the median lies between the 10th and 11th numbers. Both the 10th and 11th values are 60, so the median is 60 pages.
有 20 个数值，中位数位于第 10 和第 11 个数的中间。第 10 和第 11 个数都是 60，所以中位数为 60 页。
The mode is the value that appears most often. Looking at the frequency table, 55 and 60 both appear 4 times – more than any other number. Therefore, this data set has two modes (it is bimodal): 55 and 60 pages.
众数是出现次数最多的值。查看频数表，55 和 60 都出现了 4 次——比其他任何数字都多。因此，这组数据有两个众数（它是双峰的）：55 页和 60 页。
Here we have three different averages: mean = 62.5, median = 60, mode = 55 and 60. Each one gives a slightly different picture of the “typical” reading amount. The mean is pulled a little higher by the two students who read 80 pages, whereas the median and mode suggest slightly lower typical values.
现在我们得到了三种不同的平均数：平均数 = 62.5，中位数 = 60，众数 = 55 和 60。每一种都给出了“典型”阅读量的略微不同的图景。平均数被两个阅读 80 页的学生略微拉高了，而中位数和众数则提示稍低一些的典型数值。
8. Range and Spread | 极差和离散程度
Knowing an average is helpful, but it does not tell us how consistent the data are. The range measures the spread between the largest and smallest values. Joe calculated the range:
了解平均数很有帮助，但它并不能告诉我们数据的一致性如何。极差衡量最大值与最小值之间的分布范围。Joe 计算了极差：
Range = Maximum value – Minimum value = 80 – 45 = 35 pages
极差 = 最大值 – 最小值 = 80 – 45 = 35 页
A range of 35 pages means there is quite a wide spread in weekly reading amounts. Some students read fewer than 50 pages, while others read 80. If the range were very small, say 10 pages, we would know that most students read similar amounts; a large range tells us there is considerable variation in reading habits within the class.
35 页的极差意味着每周阅读量存在相当大的分布范围。一些学生阅读不足 50 页，而另一些则达到 80 页。如果极差很小，比如 10 页，我们就知道多数学生的阅读量相近；很大的极差则告诉我们班级内部的阅读习惯存在显著差异。
To describe spread more fully, statisticians also use measures like the interquartile range, but for Year 7 the range gives a good starting insight into variability.
为了更全面地描述离散程度，统计学家还会使用诸如四分位距等度量，但对于 Year 7 而言，极差已经能为变异性提供良好的初步认识。
9. Interpreting Results | 结果解读
With all the statistics calculated, Joe can now answer his original question. On average, students read between about 55 and 63 pages per week, depending on which average you use. The most common amounts reported were 55 and 60 pages. However, there is variation: a few students read as few as 45 pages and a couple read as many as 80.
计算完所有统计量后，Joe 现在可以回答他最初的问题了。平均而言，学生们每周阅读 55 到 63 页左右，具体取决于你使用的平均数。最常见的报告量是 55 页和 60 页。然而，也存在差异：少数学生只读了 45 页，而有两名同学读到了 80 页之多。
Joe might conclude that most Year 7 students in his class are reading a reasonable amount each week, but he could also use this evidence to encourage the class to set a weekly reading target of 65 pages. He may wonder whether students who read more pages tend to perform better in English – a question for another investigation.
Joe 可以得出结论：他所在班级的大多数 Year 7 学生每周的阅读量是合理的，但他也可以利用这一证据鼓励全班设定每周 65 页的阅读目标。他可能会想知道，阅读页数更多的学生是否在英语学科上表现更好——这是另一个调查可以探讨的问题。
When interpreting results, it is important to remember the limitations: the data come from just one class of 20 students, so they may not represent all Year 7 students. Also, the values were self‑reported and might contain some inaccuracy if students rounded or guessed their page counts.
在解读结果时，重要的是要记住其局限性：数据仅来自一个班级的 20 名学生，因此可能无法代表所有 Year 7 学生。此外，这些数值是自我报告的，如果学生们对页数进行了四舍五入或估计，可能会含有一些不准确之处。
10. Conclusion and Reflection | 结论与反思
This case study has walked you through a complete statistical investigation – from asking a question and gathering data to organising, displaying, and analysing it. You have seen how frequency tables, bar charts, pie charts, the mean, median, mode and range each contribute a piece of the puzzle. Together they give a much richer picture than any single number alone.
本次案例分析带你经历了一次完整的统计调查——从提出问题、收集数据，到整理、展示和分析数据。你已经看到频数表、条形图、饼图、平均数、中位数、众数和极差如何各自贡献了拼图的一部分。它们共同描绘出的图景比任何单一数字都要丰富得多。
Reflecting on the process, Joe realised that a well‑planned survey yields clear answers, but every dataset has its quirks. Being careful at the data‑entry stage, checking totals, and thinking critically about what the averages really mean are all vital skills that will continue to develop throughout your SQA Statistics journey.
反思这一过程，Joe 意识到精心设计的调查能产生清晰的答案，但每个数据集都有其独特之处。在数据录入阶段仔细核对、检查总数、批判性地思考平均数真正的含义，这些都是在你的 SQA 统计学习旅程中需要持续培养的关键技能。
We encourage you to design your own small survey, collect some data, and apply the same steps. Practice makes the process feel natural, and soon you will be able to tackle any statistical case study with confidence.
我们鼓励你设计自己的小型调查，收集一些数据，并应用相同的步骤。练习会让这个过程变得自然，很快你就能充满信心地应对任何统计案例分析。
Published by TutorHao | Statistics Revision Series | aleveler.com
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