📚 Year 7 Cambridge Statistics: Case Study Practical Exercise | 剑桥 7 年级统计：案例分析实战演练
Statistics is a powerful tool that helps us make sense of the world by collecting, organising, displaying and interpreting data. In this case study, you will play the role of a young data analyst investigating how much time a group of Year 7 students spends on screens each day. You will follow every step of a real statistical investigation – from designing a survey and gathering raw data to drawing graphs, calculating averages and making evidence-based conclusions. This practical exercise will strengthen your understanding of frequency tables, bar charts, pie charts, mean, median, mode and range, exactly as required by the Cambridge Year 7 curriculum. Let’s get started and turn numbers into meaningful insights!
统计学是一个强大的工具，它通过收集、整理、展示和解释数据来帮助我们理解世界。在本案例研究中，你将扮演一位年轻的数据分析师，调查一群七年级学生每天花在屏幕上的时间。你将遵循一次真实统计调查的每一个步骤——从设计调查问卷、收集原始数据，到绘制图表、计算平均值并得出基于证据的结论。这次实战演练将强化你对频率表、条形图、饼图、平均数、中位数、众数和范围的理解，完全符合剑桥 7 年级课程的要求。让我们马上开始，把数字变成有意义的见解吧！
1. Setting the Scene: The Screen Time Survey | 情景设定：屏幕时间调查
Screen time has become an important topic in health and education. Teachers and parents often wonder how many hours students spend on phones, tablets, computers and televisions each day. To explore this question, a Year 7 class decided to carry out a statistical investigation. They wanted to collect accurate data, summarise it using different statistical measures and present their findings clearly. The main question was: ‘How many hours per day do students in our class spend on screens (including phones, gaming, TV and homework)?’ This real‑world context makes the numbers feel relevant and helps you see why we learn statistics.
屏幕时间已成为健康和教育领域的一个重要话题。老师和家长常常想知道学生每天花在手机、平板电脑、电脑和电视上的时间有多少。为了探究这个问题，一个七年级班级决定开展一项统计调查。他们想要收集准确的数据，用不同的统计量来概括数据，并清晰地展示他们的发现。主要的问题是：“我们班的学生每天花在屏幕上的时间（包括手机、游戏、电视和做作业）有多少小时？”这个真实的情境让数字变得亲切，也让你明白为什么我们要学习统计。
2. Collecting the Data | 收集数据
The class designed a simple survey. Each student was asked to record the number of hours they spent on screens on a typical school day, rounded to the nearest half-hour where needed. Twenty students took part. The raw data, in hours, were recorded in the order they were collected: 2, 3, 1, 4, 2.5, 3, 2, 1.5, 4, 3.5, 2, 2, 3, 2.5, 1, 3, 4, 2, 3.5, 3. At first glance, this list is messy – some values appear several times, others only once. Before we can draw any conclusions, we need to organise the data.
班级设计了一份简单的问卷。每个学生被要求记录他们在普通上学日花在屏幕上的小时数，必要时四舍五入到最近的半小时。共有二十名学生参与。原始数据（以小时为单位）按收集的顺序记录如下：2, 3, 1, 4, 2.5, 3, 2, 1.5, 4, 3.5, 2, 2, 3, 2.5, 1, 3, 4, 2, 3.5, 3。乍一看，这份清单杂乱无章——有些数值出现了好几次，有些只出现一次。在得出任何结论之前，我们需要整理这些数据。
A good practice in data collection is to keep a clear record of how the data were gathered. We always note the date, the number of participants and any rounding rules used. In this case, we know there are exactly 20 data points, and values are given to one decimal place where a half-hour was recorded. This transparency makes the investigation reliable and allows others to repeat it.
数据收集的一个好习惯是清楚记录数据的收集方式。我们总是记下日期、参与者人数以及所使用的任何舍入规则。在这个案例中，我们知道正好有 20 个数据点，数值保留一位小数来记录半小时。这种透明度使调查变得可靠，也让别人可以重复这项调查。
3. Organising Data with a Frequency Table | 用频率表整理数据
A frequency table helps us see how many times each data value occurs. First, we list all the distinct screen‑time values that appear in the raw data: 1, 1.5, 2, 2.5, 3, 3.5 and 4 hours. Then, we count the frequency for each value. The count, or tally, shows us the distribution at a glance. The table below presents the organised data. Notice how the table transforms the messy list into a clear summary.
频率表能帮助我们看清每个数据值出现了多少次。首先，我们列出原始数据中所有不同的屏幕时间值：1, 1.5, 2, 2.5, 3, 3.5 和 4 小时。然后，我们数出每个值的频数。计数（或划记）让我们一眼就能看出分布情况。下面的表格展示了整理好的数据。请注意，表格如何把杂乱无章的清单变成了清晰的汇总。
| Screen Time (hours) | Tally | Frequency |
|---|---|---|
| 1.0 | || | 2 |
| 1.5 | | | 1 |
| 2.0 | |||| | 5 |
| 2.5 | || | 2 |
| 3.0 | |||| | 5 |
| 3.5 | || | 2 |
| 4.0 | ||| | 3 |
From the frequency table we can quickly spot that 2 hours and 3 hours are the most common screen‑time lengths, each occurring 5 times. The least common value is 1.5 hours, appearing only once. The total frequency adds up to 20, which matches the number of students surveyed. Checking the total frequency is a simple but important way to verify that no data have been lost.
从频率表中我们可以迅速发现，2 小时和 3 小时是最常见的屏幕时间时长，各自出现了 5 次。最少见的值是 1.5 小时，只出现了 1 次。总频数加起来是 20，与接受调查的学生人数一致。检查总频数是一种简单却重要的方法，可以核实没有数据遗漏。
4. Visualising Data: Bar Chart | 数据可视化：条形图
A bar chart is a perfect choice for displaying the frequency of discrete or categorical data like our screen‑time values. On the horizontal axis we place the different screen‑time categories (1, 1.5, 2, 2.5, 3, 3.5 and 4 hours). On the vertical axis we show the frequency, using a scale that goes up to at least 5. For each category we draw a bar whose height equals its frequency. The bars should be of equal width and separated by gaps to emphasise that the categories are distinct.
条形图非常适合展示像我们屏幕时间值这样的离散或分类数据的频率。在横轴上我们放置不同的屏幕时间类别（1, 1.5, 2, 2.5, 3, 3.5 和 4 小时）。在纵轴上我们显示频数，使用的刻度至少要到 5。对于每个类别，我们画一个高度等于其频数的条形。条形的宽度应该相等，并且条形之间要留有空隙，以强调各个类别是彼此独立的。
If you sketch the bar chart, you will see that the tallest bars are at 2 hours and 3 hours, both reaching a height of 5. The smallest bar stands at 1.5 hours with a height of only 1. Bar charts make it extremely easy to compare frequencies at a single glance. They are especially useful when presenting findings to an audience because patterns like peaks and gaps become immediately visible.
如果你画出示意图，你会看到最高的条形位于 2 小时和 3 小时处，两者都达到了高度 5。最小的条形位于 1.5 小时处，高度只有 1。条形图让人们一眼就能轻松比较频数。当向听众展示结果时，条形图特别有用，因为高峰和缺口等模式立刻变得一目了然。
5. Visualising Data: Pie Chart | 数据可视化：饼图
A pie chart shows the proportion of the whole that each category represents. To draw a pie chart, we need to calculate the angle for each sector. The total frequency is 20, so one student represents 360° ÷ 20 = 18° of the pie. We then multiply each frequency by 18° to find its sector angle. The table below shows the calculations. Once you have the angles, you can draw the pie chart using a protractor, labelling each slice with the screen‑time value or a percentage.
饼图显示了每个类别在整体中所占的比例。要绘制饼图，我们需要计算每个扇形的角度。总频数是 20，所以一名学生代表饼图的 360° ÷ 20 = 18°。然后我们用每个频数乘以 18° 来得出其扇形角度。下表展示了计算过程。得到角度后，你就可以用量角器画出饼图，并在每一块上标注屏幕时间值或百分比。
| Screen Time (hours) | Frequency | Sector Angle (°) |
|---|---|---|
| 1.0 | 2 | 2 × 18 = 36° |
| 1.5 | 1 | 1 × 18 = 18° |
| 2.0 | 5 | 5 × 18 = 90° |
| 2.5 | 2 | 2 × 18 = 36° |
| 3.0 | 5 | 5 × 18 = 90° |
| 3.5 | 2 | 2 × 18 = 36° |
| 4.0 | 3 | 3 × 18 = 54° |
A pie chart is excellent for showing that students who spend 2 hours and 3 hours on screens together cover half of the pie (90° + 90° = 180°). Meanwhile, the 1.5‑hour category occupies only a tiny 18° slice. Pie charts help readers quickly grasp the relative sizes of categories, but they are less useful for precise comparisons than bar charts when frequencies are close.
饼图非常适合显示，花 2 小时和 3 小时屏幕时间的学生加起来占了饼图的一半（90° + 90° = 180°）。与此同时，1.5 小时的类别只占据了小小的 18° 扇形。饼图帮助读者迅速把握各类别的相对大小，但当频数接近时，饼图不如条形图那样利于精确比较。
6. Calculating the Mean | 计算平均数
The mean, often called the average, gives us a single number that summarises the typical screen time. To find the mean, we add up all the data values and then divide by the total number of values. First, we add the 20 screen‑time hours from the raw data: 2 + 3 + 1 + 4 + 2.5 + 3 + 2 + 1.5 + 4 + 3.5 + 2 + 2 + 3 + 2.5 + 1 + 3 + 4 + 2 + 3.5 + 3 = 52.5 hours. Now we divide by the number of students, 20.
平均数，通常被称为平均值，为我们提供了一个概括典型屏幕时间的单一数字。要计算平均数，我们先把所有数据值加起来，然后除以数据值的总个数。首先，我们把原始数据中的 20 个屏幕小时数相加：2 + 3 + 1 + 4 + 2.5 + 3 + 2 + 1.5 + 4 + 3.5 + 2 + 2 + 3 + 2.5 + 1 + 3 + 4 + 2 + 3.5 + 3 = 52.5 小时。现在我们用这个和除以学生人数 20。
Mean = (Sum of all values) ÷ (Number of values) = 52.5 ÷ 20 = 2.625 hours
So the mean screen time is 2.625 hours, which we can also write as about 2 hours and 38 minutes. The mean is useful because it takes every single value into account. However, it can be pulled up or down by extremely large or small values – in this dataset a student with 4 hours of screen time increases the mean, while a 1‑hour student brings it down. That is why we also need other measures like the median and mode to get a fuller picture of the data.
因此，平均屏幕时间是 2.625 小时，我们也可以写成大约 2 小时 38 分钟。平均数很有用，因为它考虑了每一个数值。然而，极端的大值或小值可能会把它拉高或拉低——在这个数据集中，一个屏幕时间为 4 小时的学生会拉高平均数，而一个 1 小时的学生则会拉低它。这就是为什么我们还需要中位数和众数等其他度量，以便更全面地了解数据。
7. Finding the Median | 找出中位数
The median is the middle value when all the data are arranged in order. If there is an even number of values, the median is the mean of the two middle numbers. Let’s sort the 20 screen‑time values from smallest to largest: 1.0, 1.0, 1.5, 2.0, 2.0, 2.0, 2.0, 2.0, 2.5, 2.5, 3.0, 3.0, 3.0, 3.0, 3.0, 3.5, 3.5, 4.0, 4.0, 4.0. Since we have 20 values, the median lies between the 10th and 11th values.
中位数是所有数据按顺序排列后位于中间的值。如果数值的个数为偶数，中位数就是中间两个数的平均值。让我们把这 20 个屏幕时间值从小到大排序：1.0, 1.0, 1.5, 2.0, 2.0, 2.0, 2.0, 2.0, 2.5, 2.5, 3.0, 3.0, 3.0, 3.0, 3.0, 3.5, 3.5, 4.0, 4.0, 4.0。因为有 20 个值，中位数位于第 10 个和第 11 个值之间。
10th value = 2.5, 11th value = 3.0, so Median = (2.5 + 3.0) ÷ 2 = 2.75 hours
The median screen time is 2.75 hours. Notice that this is slightly higher than the mean of 2.625 hours. The median is not affected by the few very low or very high values, which makes it a better measure of the ‘typical’ value when the data are skewed. Half of the students spend 2.75 hours or less on screens, and the other half spend more.
中位屏幕时间为 2.75 小时。请注意，这比平均数 2.625 小时略高。中位数不受少数极低或极高数值的影响，这使得在数据分布偏斜时，它能更好地反映“典型”值
Published by TutorHao | Year 7 统计 Revision Series | aleveler.com
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