Case Study: Investigating Year 7 Students' Screen Time | 案例研究：调查七年级学生的屏幕时间

📚 Case Study: Investigating Year 7 Students’ Screen Time | 案例研究：调查七年级学生的屏幕时间

In this case study, we will carry out a complete statistical investigation into the daily screen time of Year 7 students. You will see how a real question leads to designing a survey, collecting data, creating tables and charts, calculating averages and the range, and even using the data to talk about probability. The aim is to help you practise every important statistics skill you need for CCEA Year 7.

在本案例研究中，我们将完成一项针对七年级学生每日屏幕时间的完整统计调查。你将看到如何从一个真实的问题出发，设计问卷、收集数据、制作表格和图表，计算平均数、中位数、众数和范围，甚至用这些数据来讨论概率。本案例旨在帮助你练习 CCEA 七年级所有重要的统计学技能。

1. Introduction to the Case Study | 案例研究简介

Statistics is not just about numbers in a textbook – it helps us understand the world around us. A case study brings together all the stages of a statistical enquiry: posing a question, gathering information, processing the data, presenting it visually and drawing conclusions. Today we focus on a topic that affects almost every 11- and 12-year-old: screen time. By the end of this case study, you will have worked through a full investigation, from raw responses to a final written summary.

统计不仅仅是课本上的数字，它帮助我们理解周围的世界。案例研究将一次完整的统计调查所有阶段串联起来：提出问题、收集信息、处理数据、可视化呈现并得出结论。今天我们聚焦一个几乎和所有十一二岁孩子都相关的话题：屏幕时间。通过这个案例，你将完成一次完整的调查，从原始回答一直到最终的书面总结。

We will imagine that a Year 7 class decided to answer the question: “How many hours per day do students in our year group spend looking at screens?” The screens include television, computers, tablets and smartphones. The same approach can be used for any survey you design yourself, whether it is about favourite sports, pets or reading habits.

我们将想象一个七年级班级决定回答这样一个问题：”我们年级的学生每天花多少小时看屏幕？” 屏幕包括电视、电脑、平板和智能手机。同样的方法也可以用来调查你自己设计的任何主题，比如最喜欢的运动、宠物或阅读习惯。

2. Designing the Survey | 设计调查

Before we can pick up a calculator, we need a clear research question and a simple way to collect answers. The main question is: “On a typical school day, how many hours do you spend on a screen (TV, computer, tablet, phone) for leisure?” The answer will be a whole number of hours, rounded to the nearest hour. We must make sure the question is not confusing and that everyone understands it in the same way.

在我们拿起计算器之前，需要一个清晰的研究问题和简单的答案收集方式。主要问题是：”在一个普通的上学日，你花多少小时在屏幕（电视、电脑、平板、手机）上休闲？” 答案将是一个整数小时，四舍五入到最接近的小时。我们必须确保问题不会引起混淆，且每个人理解一致。

A data collection sheet is designed with two columns: one for the student’s name (optional) and one for the number of hours. We could also use a tally chart straight away. For a reliable case study, at least 20 responses are needed so that patterns can be seen.

设计的数据收集表包含两列：一列是学生姓名（可选），另一列是小时数。我们也可以直接使用计数表。为使案例研究可信，至少需要 20 份回答才能看出规律。

3. Collecting the Data | 收集数据

Suppose the class surveyed 24 students and received the following raw data (hours per day):

假设班级调查了 24 名学生，得到了以下原始数据（每天小时数）：

2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 10

These numbers are messy at first glance, but they contain a story. The next steps will organise them so that we can see the story clearly.

这些数字乍看之下十分凌乱，但它们背后藏着故事。接下来的步骤将整理这些数据，让我们能清晰地看见那个故事。

4. Organising Data: Tally Chart and Frequency Table | 整理数据：计数与频数表

We group the data into equal intervals to make a grouped frequency table. Since our values range from 2 to 10, intervals of width 2 hours work well. We use a tally for each response and then write the total frequency.

我们把数据归入等距的组来制作分组频数表。由于数值范围从 2 到 10，以 2 小时为组距的工作效果很好。我们为每个回答画计数字符，然后写出总频数。

Screen time, h (hours)	Tally	Frequency
0 – 1		0
2 – 3	\|\|\|\|	5
4 – 5	\|\|\|\| \|\|\|\|	9
6 – 7	\|\|\|\| \|\|	7
8 – 9	\|\|	2
10 – 11	\|	1

Note that the interval “2 – 3” includes 2 and 3, but not 4. Each pupil appears in exactly one group. The total frequency is 24, matching our sample size.

注意区间 “2 – 3” 包含 2 和 3，但不包含 4。每名学生只在一个组出现。总频数为 24，与样本大小一致。

This grouped frequency table is the backbone of our later graphs. Always check that the sum of frequencies equals the number of data points.

这个分组频数表是后续图表的骨架。一定要检查频数总和是否等于数据点总数。

5. Bar Chart Display | 条形图展示

A bar chart is drawn with the grouped intervals on the horizontal axis and frequencies on the vertical axis. The bars are of equal width and gaps are left between them to show that the data are grouped.

绘制条形图时，横轴为分组区间，纵轴为频数。条形的宽度相等，并且它们之间留有间隙以表明数据是分组数据。

For our data, the tallest bar would be the “4 – 5” group with frequency 9. The “10 – 11” bar would be very short, with frequency 1. The “0 – 1” group has zero frequency, so no bar is drawn.

对照我们的数据，最高的条形是 “4 – 5″ 组，频数为 9；”10 – 11″ 组的条形会很短，频数为 1；”0 – 1” 组频数为零，因此不画条形。

The bar chart instantly tells us that most students spend between 4 and 7 hours on screens, while very few spend less than 2 hours or more than 9 hours per day.

这张条形图立刻告诉我们，大多数学生每天屏幕时间在 4 到 7 小时之间，而只有极少数学生每天少于 2 小时或超过 9 小时。

6. Pie Chart Interpretation | 饼图解读

A pie chart shows the proportion of each group as a slice of a circle. To draw it, we convert each frequency into an angle using the formula:

饼图将每个组的占比用圆形切片表示。绘制时，我们使用公式将每个频数转换为角度：

Angle = (Frequency ÷ Total frequency) × 360°

For the “4 – 5” group: (9 ÷ 24) × 360° = 135°. For “6 – 7”: (7 ÷ 24) × 360° = 105°. The “2 – 3” group gets 75°, “8 – 9” gets 30°, and “10 – 11” gets 15°. The zero group gets 0°.

“4 – 5″ 组：(9 ÷ 24) × 360° = 135°；”6 – 7″ 组：(7 ÷ 24) × 360° = 105°；”2 – 3″ 组 75°；”8 – 9″ 组 30°；”10 – 11” 组 15°。零频数组为 0°。

The largest slice represents the most common screen time category. When interpreting the pie chart, we look for the mode group and compare the slices to describe the distribution.

最大的扇形代表最常见的屏幕时间类别。解读饼图时，我们寻找众数组并比较各个扇形来描述数据的分布。

7. Measures of Central Tendency: Mode, Median, Mean | 集中趋势度量：众数、中位数、均值

The mode is the value that appears most often. From the raw list, 5 hours occurs five times, more than any other number. So the mode is 5 hours.

众数是出现次数最多的值。从原始列表看，5 小时出现了五次，多于其他任何数值，因此众数为 5 小时。

For the median we order the 24 numbers from smallest to largest: 2,2,3,3,3,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,10. Because there is an even number of values, the median is the mean of the 12th and 13th values. Both are 5, so the median is 5 hours.

计算中位数时，我们将 24 个数字从小到大排列：2,2,3,3,3,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,10。因为数值个数为偶数，中位数是第 12 和第 13 个数的均值。两者都是 5，所以中位数是 5 小时。

The mean is calculated by adding all values together and dividing by the total number of values. The sum is 125 hours, and 125 ÷ 24 ≈ 5.21 hours.

Mean = Total sum ÷ Number of values = 125 ÷ 24 ≈ 5.21 hours

均值通过将所有值相加再除以值的总个数来计算。总和为 125 小时，125 ÷ 24 ≈ 5.21 小时。

The three averages are close together, which suggests the data are fairly symmetric without extreme outliers.

三个平均数十分接近，这表明数据相当对称，没有出现极端异常值。

8. Finding the Range | 计算范围

The range measures the spread of the data. It is found by subtracting the smallest value from the largest value.

范围衡量数据的分散程度，通过最大值减去最小值得到。

Range = Maximum – Minimum = 10 – 2 = 8 hours

In our case, the maximum screen time is 10 hours and the minimum is 2 hours, giving a range of 8 hours. A large range tells us there is a big difference between the lightest and heaviest screen users.

在我们的例子中，最大屏幕时间为 10 小时，最小为 2 小时，范围是 8 小时。较大的范围说明轻度使用者和重度使用者之间存在很大差异。

The range is useful, but it can be affected by just one unusual value. That is why we also look at the interquartile range in later years; for now, range gives a simple first look at spread.

范围虽然有用，但容易被单个不寻常的数值影响。这也是为什么以后我们还会看四分位距；目前，范围对我们了解数据分散程度提供了简单的第一印象。

9. Comparative Discussion | 比较讨论

If we compare the averages and the range, we can describe the typical screen time of a Year 7 student in this sample. The modal and median screen time is 5 hours, while the mean is only slightly higher at 5.21 hours, which means the distribution is quite balanced.

如果我们对比这些平均数和范围，就可以描述出此样本中七年级学生典型的屏幕时间。众数和中位数都是 5 小时，而均值只略高，为 5.21 小时，说明分布相当均衡。

The grouped frequency table and bar chart show that the most populated group is 4-5 hours, closely followed by 6-7 hours. Over two thirds of the students fall into these two groups. Very few students report very low or very high screen time. This could be used as a starting point for discussion about healthy screen habits.

分组频数表和条形图显示，人数最多的组是 4-5 小时，紧随其后的是 6-7 小时组。超过三分之二的学生落在这两个组中。只有极少数学生报告了极低或极高的屏幕时间。这个结果可作为讨论健康屏幕习惯的起点。

You could extend the case study by comparing subgroups, for example boys versus girls or weekdays versus weekends.

你还可以通过比较子组来延伸案例研究，例如男生与女生对比，或平日与周末对比。

10. Probability in Context | 情景中的概率

We can use the collected data to estimate the chance that a randomly selected student from this class spends at least 5 hours on screens. Count how many students reported 5 hours or more: 5 (for 5h), 4 (for 6h), 3 (for 7h), 2 (for 8h) and 1 (for 10h) gives a total of 15 students. So the relative frequency is 15 out of 24.

我们可以用收集到的数据来估计从这个班级随机抽取一名学生，其屏幕时间至少 5 小时的概率。数一数有多少学生报告了 5 小时及以上：5 小时有 5 人，6 小时 4 人，7 小时 3 人，8 小时 2 人，10 小时 1 人，共 15 人。因此相对频数是 24 分之 15。

Probability (screen time ≥ 5 h) = 15/24 = 5/8 = 0.625

This means there is about a 62.5% chance. In a similar way, you could work out the probability that a student spends more than 8 hours on screens: only the 8-9 and 10-11 groups count, so (2+1)/24 = 3/24 = 1/8 = 0.125.

这意味着大约有 62.5% 的可能性。用类似的方法，你可以计算出学生屏幕时间超过 8 小时的概率：只有 8-9 和 10-11 组符合，所以 (2+1)/24 = 3/24 = 1/8 = 0.125。

This is experimental probability based on real data, and it helps us make predictions about the class.

这是基于真实数据的实验概率，它帮助我们对该班级做出预测。

11. Conclusion and Reflection | 结论与反思

Through this case study we have moved from a simple question to a fully analysed set of data. We designed a survey, collected raw responses, built a grouped frequency table, displayed the data with a bar chart and a pie chart, calculated the mode, median, mean and range, and even touched on probability.

通过这个案例研究，我们从简单的问题出发，获得了一整套经过完整分析的数据。我们设计了调查问卷，收集了原始回答，制作了分组频数表，用条形图和饼图展示了数据，计算了众数、中位数、均值和范围，甚至还触及了概率。

The most important lesson is that statistics is a cycle: you ask a question, collect data, process it, present it and then interpret it. Each stage must be done carefully so that the final conclusions are fair and useful. Now it is your turn – pick a topic, design your own survey and repeat the process with real data from your class or school.

最重要的一课是，统计是一个循环：提出问题、收集数据、处理数据、呈现数据，然后解读数据。每一个阶段都必须仔细完成，这样最后的结论才能公正有用。现在轮到你了——挑选一个主题，设计你自己的问卷，并用班级或学校里的真实数据重复这个过程。

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Case Study: Investigating Year 7 Students’ Screen Time | 案例研究：调查七年级学生的屏幕时间