Year 9 SQA Statistics: Case Study Practice | SQA 九年级统计：案例分析实战演练

📚 Year 9 SQA Statistics: Case Study Practice | SQA 九年级统计：案例分析实战演练

Welcome to this practical case study revision for SQA Year 9 Statistics. We will work through a complete investigation, from designing a question to drawing conclusions, using real-world data about screen time and exercise. This step-by-step guide will help you master key statistical skills such as calculating averages, measuring spread, creating charts and understanding probability.

欢迎来到SQA九年级统计的实战案例复习。我们将通过一个完整的调查过程，从设计问题到得出结论，使用关于屏幕时间与锻炼的真实数据。这份逐步指南将帮助你掌握关键统计技能，包括计算平均数、衡量离散程度、绘制图表以及理解概率。

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1. Introducing the Investigation | 调查介绍

A Year 9 teacher wants to find out if there is a link between the time students spend on social media and their physical activity levels. The investigation question is: ‘How many hours per day do Year 9 students spend on social media, and is there a difference between boys and girls?’ She also plans to compare exercise habits.

一位九年级老师想了解学生使用社交媒体的时间与体育活动水平之间是否存在联系。调查问题是：“九年级学生每天花多少小时在社交媒体上？男女生之间是否有差异？”她还计划比较锻炼习惯。

This is a statistical enquiry involving data collection, organisation, analysis and interpretation. By following the investigation, you will see how each stage links together.

这是一个涉及数据收集、整理、分析和解释的统计探究。通过跟踪调查，你将看到每个阶段是如何联系在一起的。

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2. Collecting Relevant Data | 收集相关数据

The teacher surveyed 20 students randomly selected from Year 9. Each student reported their daily social media hours (to the nearest half hour) and their weekly exercise hours. The data for social media hours is shown below, along with gender.

老师随机调查了20名九年级学生。每名学生报告了他们每天使用社交媒体的时长（精确到半小时）以及每周锻炼小时数。以下是社交媒体时长的数据以及性别信息。

Student	Gender	Social Media (h)
1	Girl	0.5
2	Girl	1.0
3	Boy	1.0
4	Girl	1.5
5	Girl	1.5
6	Boy	2.0
7	Girl	2.0
8	Boy	2.0
9	Girl	2.5
10	Boy	2.5
11	Girl	2.5
12	Girl	2.5
13	Boy	3.0
14	Boy	3.0
15	Girl	3.0
16	Boy	3.5
17	Boy	4.0
18	Boy	4.0
19	Boy	4.5
20	Boy	5.0

This raw data is the starting point for our whole investigation. Notice that there are 10 girls and 10 boys, which makes comparison fairer.

这些原始数据是我们整个调查的起点。请注意，女生和男生各有10人，这使得比较更加公平。

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3. Creating a Frequency Table | 制作频率表

To see patterns, we group the social media hours into intervals: 0–1 (excluding 1), 1–2, 2–3, 3–4 and 4–5 hours. Counting the data values gives the frequency for each group.

为了发现规律，我们将社交媒体时长划分为区间：0–1（不含1）、1–2、2–3、3–4和4–5小时。统计每个区间内的数据个数就得到了频数。

Time (hours)	Tally	Frequency
0 ≤ t < 1	|	1
1 ≤ t < 2	||||	4
2 ≤ t < 3	|||| ||	7
3 ≤ t < 4	||||	4
4 ≤ t ≤ 5	||||	4

Frequency tables make it simpler to identify the most common range (2–3 hours) and to draw charts later.

频率表让我们更容易看出最常见的区间（2–3小时），也便于后续画图。

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4. Calculating the Mean | 计算均值

The mean is the average found by adding all values and dividing by the total number of data points. Here the sum is 0.5 + 1.0 + 1.0 + 1.5 + 1.5 + 2.0 + 2.0 + 2.0 + 2.5 + 2.5 + 2.5 + 2.5 + 3.0 + 3.0 + 3.0 + 3.5 + 4.0 + 4.0 + 4.5 + 5.0 = 51.5 hours.

均值是通过将所有数值相加再除以数据总个数得到的平均数。这里的总和是0.5 + 1.0 + 1.0 + 1.5 + 1.5 + 2.0 + 2.0 + 2.0 + 2.5 + 2.5 + 2.5 + 2.5 + 3.0 + 3.0 + 3.0 + 3.5 + 4.0 + 4.0 + 4.5 + 5.0 = 51.5小时。

Mean = 51.5 ÷ 20 = 2.575 hours

So the typical Year 9 student in this survey spends about 2.6 hours per day on social media. The mean is sensitive to extreme values like 5.0 hours.

因此，本次调查中九年级学生每天平均花费约2.6小时在社交媒体上。均值对5.0小时这样的极端值很敏感。

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5. Finding the Median and Mode | 求中位数和众数

After sorting the data, the median is the middle value. With 20 values, it is the average of the 10th and 11th values: both are 2.5. Hence the median = 2.5 hours. The mode, the most frequent value, is also 2.5 (appearing 4 times).

将数据排序后，中位数是中间的值。有20个数据，因此取第10和第11个数据的平均值：两者都是2.5，所以中位数 = 2.5小时。众数，即出现次数最多的值，也是2.5（出现4次）。

When the mean (2.575) is close to the median (2.5) and mode, the distribution is roughly symmetrical. This trio gives a complete picture of the data’s centre.

当均值（2.575）接近中位数（2.5）和众数时，分布大致对称。这三个指标共同描绘了数据的中心位置。

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6. Measuring Spread: Range | 衡量离散程度：极差

The range shows how spread out the data are. It is simply the difference between the maximum and minimum values. Here max = 5.0, min = 0.5, so the range = 5.0 − 0.5 = 4.5 hours.

极差显示数据的分散程度。它就是最大值与最小值之差。这里最大值5.0，最小值0.5，所以极差 = 5.0 − 0.5 = 4.5小时。

A large range indicates wide variation in screen time habits among students. We will later compare ranges between boys and girls to see if one group is more consistent.

极差很大，表明学生之间屏幕时间习惯差异显著。稍后我们会比较男生和女生的极差，看看哪一组更一致。

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7. Visualising Data with Bar Charts | 用条形图可视化数据

Using the frequency table, we can draw a bar chart with intervals on the horizontal axis and frequency on the vertical axis. Each bar’s height represents the number of students in that group.

利用频率表，我们可以绘制条形图，横轴为区间，纵轴为频数。每个条形的高度代表该组的学生人数。

The tallest bar is for 2–3 hours, confirming that this is the most common screen time category. Bar charts make it easy to compare categories at a glance.

最高的条形是2–3小时组，证实这是最常见的屏幕时间类别。条形图使得类别间的比较一目了然。

Always label axes, give the chart a title, and use equal spacing between bars. (Imagine a bar chart with categories 0–1, 1–2, 2–3, 3–4, 4–5 and frequencies 1, 4, 7, 4, 4.)

务必标记坐标轴，给图表加上标题，并保持条形之间等间距。（请想象一个条形图，类别为0–1、1–2、2–3、3–4、4–5，频数分别为1、4、7、4、4。）

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8. Displaying Proportions with Pie Charts | 用饼图表示比例

A pie chart shows how the whole sample is divided. For each group, the sector angle = (frequency ÷ 20) × 360°. For example, the 2–3 hour group: (7 ÷ 20) × 360° = 126°. The 0–1 hour sector is (1 ÷ 20) × 360° = 18°.

饼图能显示整个样本的划分。每个组的扇形角度 =（频数 ÷ 20）× 360°。例如，2–3小时组：（7 ÷ 20）× 360° = 126°。0–1小时组的扇形角度为（1 ÷ 20）× 360° = 18°。

Calculating angles: 1–2 hours: (4 ÷ 20) × 360° = 72°; 3–4 hours: 72°; 4–5 hours: 72°. Check: 18° + 72° + 126° + 72° + 72° = 360°. Pie charts are excellent for showing relative sizes, but they don’t give exact frequencies.

角度计算：1–2小时：（4 ÷ 20）× 360° = 72°；3–4小时：72°；4–5小时：72°。验证：18° + 72° + 126° + 72° + 72° = 360°。饼图非常适合展示相对大小，但不提供确切频数。

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9. Comparing Two Groups | 比较两组数据

The teacher wants to know if boys and girls have different screen time patterns. Separating the data gives two sets: Girls: 0.5, 1.0, 1.5, 1.5, 2.0, 2.5, 2.5, 2.5, 3.0, 3.0. Boys: 1.0, 2.0, 2.0, 2.5, 3.0, 3.0, 3.5, 4.0, 4.0, 4.5, 5.0 (note 11? Actually we listed 20 students: check original table. I have 10 girls and 10 boys: girls: 0.5,1.0,1.5,1.5,2.0,2.5,2.5,2.5,3.0,3.0 – yes 10. Boys: 1.0,2.0,2.0,2.5,3.0,3.0,3.5,4.0,4.0,4.5,5.0 – that’s 11? Let’s recount from table: students 3 boy 1.0, 6 boy 2.0, 8 boy 2.0, 10 boy 2.5, 13 boy 3.0, 14 boy 3.

Published by TutorHao | Year 9 统计 Revision Series | aleveler.com

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