Cambridge Year 8 Statistics: Screen Time Case Study in Action | Year 8 剑桥统计：屏幕时间案例分析实战演练

📚 Cambridge Year 8 Statistics: Screen Time Case Study in Action | Year 8 剑桥统计：屏幕时间案例分析实战演练

In this case study, we put statistical concepts into real-world practice. You will step into the shoes of a data detective investigating whether the amount of time students spend on electronic devices each day is linked to their mathematics performance. By following a complete statistical investigation—from designing a data collection plan and organising raw numbers to drawing scatter graphs and making probability statements—you will see how every skill you have learned in Year 8 statistics fits together. This hands‑on approach turns abstract formulas into powerful tools for answering genuine questions.

在这个案例分析中，我们会把统计概念用于解决真实问题。你将扮演一名“数据侦探”，调查学生每天使用电子设备的时间是否与他们的数学成绩有关。从设计数据收集方案、整理原始数据，到绘制散点图、计算概率，你将完整经历一次统计调查，亲眼看到 Year 8 统计课上学到的每一项技能是如何协同工作的。这种动手实践的方式能把抽象的公式变成回答现实问题的有力工具。

1. Introducing the Case: Screen Time and Maths Scores | 案例背景：屏幕时间与数学成绩

A class of 24 Year 8 students was chosen for a small‑scale survey. Each student reported the number of hours they typically spend on electronic devices (phones, tablets, gaming consoles) per day, and their most recent mathematics test score (out of 50) was taken from the school records. The research question was: ‘Is there a relationship between daily screen time and maths achievement?’ The data set is shown in Table 1.

我们从一个 24 名 Year 8 学生的班级中进行了一项小规模调查。每名学生报告了自己通常每天花在电子设备上（手机、平板、游戏机）的时长，并从学校记录中提取了他们最近一次数学测验的成绩（满分 50 分）。研究问题是：“每日屏幕时间与数学成绩有关吗？” 数据集见表 1。

Student	Screen Time (h)	Maths Score (/50)	Student	Screen Time (h)	Maths Score (/50)
1	2.5	38	13	3.8	29
2	3.0	35	14	4.2	26
3	1.5	42	15	5.5	20
4	4.0	28	16	1.8	43
5	2.0	40	17	3.8	29
6	5.0	25	18	4.8	24
7	3.5	32	19	2.0	37
8	4.5	22	20	5.2	21
9	1.0	45	21	1.2	46
10	2.8	33	22	3.9	27
11	6.0	18	23	6.5	15
12	3.2	30	24	0.8	48

Table 1: Raw data from the screen time and maths score survey. 屏幕时间与数学成绩调查原始数据。

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2. Data Collection and Sampling | 数据收集与抽样方法

In any statistical investigation, we must be clear about how the data were gathered. Here, the data come from a convenience sample—one accessible Year 8 class. The screen times were self‑reported, which means students estimated their own usage; the maths scores were taken from official test records, so they are more objective. The target population could be all Year 8 students in the school, but our sample represents only one class. Therefore, any conclusions we draw apply strictly to this class unless we collect more data.

在任何统计调查中，我们都必须清楚数据是如何收集的。这组数据来自一个“便利样本”——即一个容易接触到的 Year 8 班级。屏幕时间由学生自我报告，这意味着他们自行估计了自己的使用时间；数学成绩则来自学校正式记录，更为客观。目标总体可能是全校的所有 Year 8 学生，但我们的样本只代表这一个班级。因此，除了收集更多数据，我们得到的任何结论都只严格适用于这个班级。

When planning a similar study, you should consider random sampling methods—such as drawing names from a hat or using a random number generator—to reduce bias. Additionally, a larger sample size would make the findings more reliable and allow us to generalise more confidently.

如果设计类似的研究，你应该考虑随机抽样方法——例如从帽子中抽签或使用随机数生成器——以减少偏差。此外，更大的样本量会让结果更加可靠，也让我们更有把握进行推广。

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3. Organising Raw Data into Frequency Tables | 将原始数据整理成频数表

Raw data can be hard to interpret. Grouping the screen times into intervals gives a clearer picture of how the values are distributed. We choose class intervals of width 1 hour: 0–0.9, 1.0–1.9, 2.0–2.9, 3.0–3.9, 4.0–4.9, 5.0–5.9 and 6.0–6.9. Tally the number of students in each group to build a frequency table.

原始数据往往难以直接解读。把屏幕时间分组后，数值的分布就清晰多了。我们选择组距为 1 小时：0–0.9, 1.0–1.9, 2.0–2.9, 3.0–3.9, 4.0–4.9, 5.0–5.9 和 6.0–6.9。统计每组中的人数，就得到频数表。

Screen Time (hours)	Tally	Frequency
0.0 – 0.9	|	1
1.0 – 1.9	||||	4
2.0 – 2.9	|||||	4
3.0 – 3.9	||||||	6
4.0 – 4.9	||||	4
5.0 – 5.9	|||	3
6.0 – 6.9	||	2

From the grouped frequency table we can immediately see that the most common screen time interval is 3.0–3.9 hours, and that very few students report less than 1 hour or more than 6 hours of daily screen use.

从分组频数表可以立即看出，最常见的屏幕时间区间是 3.0–3.9 小时，而极少数学生每天屏幕时间少于 1 小时或多于 6 小时。

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4. Measures of Central Tendency: Mean, Median and Mode | 集中趋势量数：平均数、中位数与众数

To summarise the typical screen time, we calculate the three averages.

为概括屏幕时间的典型水平，我们计算三种平均数。

The mean is found by adding all 24 values and dividing by 24: Sum = 80.9 hours, so

Mean = 80.9 / 24 ≈ 3.37 hours

均值由 24 个数值求和后除以 24 得到：总和 = 80.9 小时，因此

均值 = 80.9 / 24 ≈ 3.37 小时

For the median, we list the data in order: 0.8, 1.0, 1.2, 1.5, 1.8, 2.0, 2.0, 2.2, 2.5, 2.8, 3.0, 3.2, 3.5, 3.8, 3.9, 4.0, 4.2, 4.5, 4.8, 5.0, 5.2, 5.5, 6.0, 6.5. With 24 values (an even number), the median is the mean of the 12th and 13th values: (3.2 + 3.5)/2 = 3.35 hours.

对于中位数，我们把数据从小到大排列。有 24 个值（偶数），中位数是第 12 和第 13 个值的平均数：(3.2 + 3.5)/2 = 3.35 小时。

The mode is the value that appears most frequently. A screen time of 2.0 hours appears twice, while all other exact values appear only once; hence the mode is 2.0 hours. Notice that the mean and median are close to each other, but the mode is lower, suggesting the distribution is slightly skewed to the right.

众数是出现次数最多的值。2.0 小时出现了两次，而其他数值只出现一次，所以众数是 2.0 小时。可以看到均值和中位数很接近，但众数偏低，说明分布略向右偏。

For maths scores, the mean is 763/24 ≈ 31.8 marks; the median lies between the 12th and 13th ordered scores (30 and 32), giving 31 marks; and there is no repeated score, so no clear mode.

就数学成绩而言，均值为 763/24 ≈ 31.8 分；中位数位于第 12 和第 13 个有序分数的中间 (30 和 32)，得 31 分；所有分数均不重复，因此没有明显的众数。

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5. Measures of Spread: Range | 离散程度：极差（范围）

While the mean tells us about a typical value, the range tells us about the spread of the data.

均值描述的是典型值，而极差（范围）描述的是数据的分散程度。

For screen time: the maximum is 6.5 hours, the minimum is 0.8 hours, so

Range = 6.5 – 0.8 = 5.7 hours

对于屏幕时间：最大值 6.5 小时，最小值 0.8 小时，因此

极差 = 6.5 – 0.8 = 5.7 小时

For maths scores: maximum 48, minimum 15, so the range is 33 marks. A large range for maths suggests that pupils’ achievement varied widely within this class.

对于数学成绩：最大值 48，最小值 15，极差为 33 分。较大的极差表明这个班级内部学生的成绩差异很大。

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6. Visualising a Single Variable: Bar Chart of Screen Time | 单变量可视化：屏幕时间柱状图

A bar chart is ideal for displaying the frequency distribution of grouped data. Using the grouped frequency table, we can draw bars whose heights correspond to the frequencies. The horizontal axis shows the screen time intervals and the vertical axis shows the number of students.

柱状图非常适合展示分组数据的频数分布。利用分组频数表，我们可以以柱子的高度表示频数。横轴为屏幕时间区间，纵轴为学生人数。

From the bar chart (which you can sketch yourself), the interval 3.0–3.9 stands out as the tallest bar, confirming the modal class. The bars gradually decrease on both sides, forming a roughly single‑peaked shape.

从柱状图（你可以自己画出来）可以明显看到，3.0–3.9 的柱体最高，确认为众数组。两侧的柱子逐渐降低，呈现出大致单峰的形态。

When you draw the chart, remember to label both axes, give the chart a title, and leave equal gaps between bars.

画图时，记得为两轴添加标签，给图表加上标题，并且在柱子之间留出等距的空隙。

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7. Exploring Two Variables: Scatter Graph of Screen Time vs. Maths Score | 探索双变量：屏幕时间与数学成绩的散点图

To see whether screen time and maths score are related, we plot each student as a point on a scatter graph, with screen time on the x‑axis and maths score on the y‑axis.

为了观察屏幕时间与数学成绩是否有关，我们将每个学生用一个点绘制在散点图上，x 轴为屏幕时间，y 轴为数学成绩。

For example, student 1 is plotted at (2.5, 38); student 6 at (5.0, 25); student 24 at (0.8, 48). When all 24 points are plotted, a pattern emerges: points drift downwards from top‑left to bottom‑right. This indicates a negative association—students with higher screen time tend to have lower maths scores.

例如，学生 1 的点位于 (2.5, 38)；学生 6 在 (5.0, 25)；学生 24 在 (0.8, 48)。当 24 个点全部画出后，一种模式出现了：点群从左上方向右下方走低。这表明存在负相关——屏幕时间较高的学生往往数学成绩较低。

The relationship is not perfectly linear; some low screen‑time students still achieved modest scores, and a few high screen‑time students scored around 30. This reminds us that correlation does not imply causation—other factors, such as study habits or sleep, may also play a role.

这种关系并非完美的线性；一些屏幕时间短的学生成绩也只是中等，而个别屏幕时间长的学生也考了约 30 分。这提醒我们：相关关系不代表因果关系——其他因素，如学习

Published by TutorHao | Year 8 统计 Revision Series | aleveler.com

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