Year 8 Edexcel Statistics: Case Study Practice | 八年级Edexcel统计：案例分析实战演练

📚 Year 8 Edexcel Statistics: Case Study Practice | 八年级Edexcel统计：案例分析实战演练

Welcome to this complete case study walkthrough, designed to help you apply every key statistical skill from the Year 8 Edexcel Statistics syllabus. You will learn by doing: from asking a question and collecting data to presenting findings and calculating probabilities. All steps are explained in both English and Chinese, with worked examples and clear reasoning.

欢迎来到这个完整的案例研究演练，旨在帮助你运用 Edexcel 八年级统计课程中的每一个关键技能。你将通过实践来学习：从提出问题、收集数据到呈现发现和计算概率。每个步骤都用中英双语解释，并配有详细的示例和清晰的推理。

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1. Defining the Statistical Question | 定义统计问题

Imagine you are a student researcher interested in how Year 8 pupils use their leisure time. You decide to focus on daily screen time spent on gaming and social media, and you suspect there might be a difference between boys and girls. A well-defined statistical question should be specific, measurable and achievable: “How does the daily screen time (in minutes) of Year 8 boys compare with that of Year 8 girls at our school?”

假设你是一名学生研究员，对八年级学生的休闲时间使用方式感兴趣。你决定关注他们每天花在游戏和社交媒体上的屏幕时间，并猜测男生和女生之间可能存在差异。一个定义清晰的统计问题应当具体、可测量且可实现：“我们学校八年级男生与女生的每日屏幕时间（以分钟计）相比如何？”

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2. Data Collection Method | 数据收集方法

To answer the question, you need primary data. You design a short questionnaire asking each pupil to record how many minutes they spent on electronic devices for entertainment yesterday. To make the sample representative, you randomly select 15 boys and 15 girls from the Year 8 register. You ensure anonymity and explain that the data will only be used for a class project.

为了回答这个问题，你需要第一手数据。你设计了一份简短问卷，要求每位学生记录昨天在电子设备上用于娱乐的分钟数。为了使样本具有代表性，你从八年级名单中随机选取了15名男生和15名女生。你确保匿名性，并说明这些数据仅用于课堂项目。

The questionnaire uses a simple open question: “How many minutes did you spend on screens for fun yesterday?” Data is collected at the start of a school day to minimise recall error. This gives you 30 data values – a manageable size for Year 8 analysis.

问卷使用一个简单的开放式问题：“你昨天用于娱乐的屏幕时间是多少分钟？”数据在上学日开始时收集，以尽量减少回忆误差。这样你得到了30个数据值——对于八年级的分析来说是一个可管理的样本量。

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3. Raw Data | 原始数据

After collecting the questionnaires, you list all the responses. The raw data for boys (in minutes) is:

收集问卷后，你列出所有回答。男生的原始数据（分钟）如下：

• 15, 30, 45, 45, 60, 60, 60, 75, 90, 90, 120, 60, 75, 90, 45

The raw data for girls (in minutes) is:

女生的原始数据（分钟）如下：

• 15, 30, 30, 45, 45, 60, 60, 60, 45, 30, 15, 45, 60, 75, 90

Having the data in two separate lists allows you to compare the groups later. Always double-check for any obvious recording mistakes before moving on.

将数据分成两个列表有助于后续进行组别比较。在进行下一步之前，请务必仔细检查是否存在明显的记录错误。

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4. Organising Data: Frequency Table | 整理数据：频数分布表

Raw data can be messy, so we create grouped frequency tables using equal class intervals: 0–19, 20–39, 40–59, 60–79, 80–99, and 100–119 minutes. Tallying the boys’ data gives:

原始数据可能显得杂乱，因此我们使用等距分组创建分组频数表：0–19、20–39、40–59、60–79、80–99 和 100–119 分钟。对男生数据进行计数后得到：

Screen time (min)	Tally	Frequency
0–19	|	1
20–39	|	1
40–59	|||	3
60–79	|||| ||	6
80–99	|||	3
100–119	|	1

Tallying the girls’ data gives:

对女生数据进行计数后得到：

Screen time (min)	Tally	Frequency
0–19	||	2
20–39	|||	3
40–59	||||	4
60–79	||||	5
80–99	|	1
100–119	–	0

Grouped tables help you see patterns at a glance. For example, boys are spread across higher intervals while girls cluster around the middle.

分组表格有助于你一目了然地看出数据的规律。例如，男生的数据分布在更高的区间，而女生则集中在中间区间。

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5. Displaying Data: Bar Chart | 数据展示：柱状图

A bar chart (or bar graph) is an excellent way to compare two data sets visually. On graph paper, draw two axes: the horizontal axis for screen time intervals and the vertical axis for frequency. Use a scale of 0 to 7 on the frequency axis and plot a pair of bars for each interval – one for boys and one for girls. Leave a small gap between each pair to show discrete groups.

柱状图是直观比较两组数据的极佳方式。在方格纸上，画出两条坐标轴：横轴表示屏幕时间区间，纵轴表示频数。在频数轴上采用 0 到 7 的刻度，为每个区间绘制一对柱形——一个代表男生，一个代表女生。在每组柱形之间留出小间隙，以显示离散的分组。

From the frequencies, you would see that the 60–79 bar is tallest for both groups, but the girls’ bar is slightly lower. Boys have a bar in the 100–119 interval, while girls do not. Always label the axes and give the chart a clear title.

根据频数，你会看到 60–79 的柱形对两个组都是最高的，但女生的柱形略低一些。男生在 100–119 区间有一个柱形，而女生没有。请务标注坐标轴，并为图表添加清晰的标题。

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6. Displaying Data: Pie Chart | 数据展示：饼图

A pie chart is useful for showing how the whole sample of 30 pupils is divided among the screen time categories. First, combine the frequencies from both groups for each interval:

饼图有助于展示 30 名学生的总样本如何在各屏幕时间类别中分布。首先，将两组各区间的频数合并：

Interval	Combined frequency	Angle = (frequency/30) × 360°
0–19	3	36°
20–39	4	48°
40–59	7	84°
60–79	11	132°
80–99	4	48°
100–119	1	12°

Using a protractor, draw each sector in order, starting from a vertical radius. Label each sector with the interval, and colour them distinctly. The pie chart immediately reveals that the 60–79 minute category is the most common, covering 132° of the circle.

使用量角器，从一条竖直半径开始，依次画出每个扇形。为每个扇形标出对应的区间，并用不同的颜色加以区分。饼图立刻显示出 60–79 分钟类别最为普遍，覆盖了圆的 132°。

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7. Calculating the Mean | 计算平均数

The mean is the average value of the data set. For boys, add all values together and divide by the number of boys (15):

平均数（均值）是数据集的平均值。对于男生，将所有数值相加，再除以男生人数（15）：

x̄_boys = (15+30+45+45+60+60+60+75+90+90+120+60+

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