KS3 WJEC Statistics: Case Study Practice | KS3 WJEC 统计：案例分析实战演练

📚 KS3 WJEC Statistics: Case Study Practice | KS3 WJEC 统计：案例分析实战演练

Welcome to this case study practice for KS3 WJEC Statistics. In this article, we will work through a real-world data scenario from a school sports day to strengthen your data handling skills. You will see how to collect, organise, display, and interpret data using the methods required by the WJEC curriculum.

欢迎来到KS3 WJEC 统计案例分析实战练习。本文将通过一个来自学校体育日的真实数据场景，强化你的数据处理技能。你将看到如何按照WJEC课程要求的方法收集、整理、展示和解释数据。

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1. Case Study Introduction: School Sports Day | 案例介绍：学校体育日

Imagine your school is holding its annual sports day, and Year 8 students are taking part in events like the 100-metre sprint, long jump, and shot put. Your task is to act as a data analyst for the long jump competition. You will collect results, summarise them, create charts, calculate averages, and even make simple probability predictions. This mirrors what a statistician does with real-life data.

想象一下，你们学校正在举办一年一度的体育日，八年级学生参加了100米短跑、跳远和铅球等项目。你的任务是担任跳远比赛的数据分析师。你将收集结果、进行汇总、绘制图表、计算平均值，甚至做出简单的概率预测。这就像是统计学家处理真实数据一样。

The learning goals for this case study are:

本次案例的学习目标是：

• Collect raw data using a recording table.

  使用记录表收集原始数据。

• Organise data into grouped frequency tables.

  将数据整理成分组频数表。

• Present data with bar charts and pie charts.

  用条形图和饼图展示数据。

• Calculate the mean, median, mode, and range.

  计算均值、中位数、众数和范围。

• Use relative frequency to estimate probabilities.

  使用相对频率估算概率。

• Write a statistical report with valid conclusions.

  撰写包含有效结论的统计报告。

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2. Collecting Data: Recording the Results | 收集数据：记录结果

Before any analysis can begin, the raw data must be recorded accurately. At the long jump event, each competitor had one official jump measured to the nearest 0.1 metre. The results for two randomly chosen groups, Team A and Team B, are shown below. A well-designed table makes the data easy to read and error-check.

在开始任何分析之前，必须准确记录原始数据。在跳远比赛中，每位选手有一次正式跳跃，测量结果精确到0.1米。以下是随机选择的两个小组——A组和B组——的成绩。一个设计良好的表格能让数据易于阅读和核对。

Here is the raw data in a structured table:

以下是结构表格中的原始数据：

Student (Team A)	Jump (m)	Student (Team B)	Jump (m)
Alex	3.2	Finley	3.6
Bailey	3.5	Gray	3.3
Casey	2.9	Harper	3.7
Drew	3.1	Jesse	3.0
Emery	3.4	Kennedy	3.2

Notice that each value is clearly labelled with its unit (m). This avoids confusion and ensures that anyone reading the table knows exactly what the numbers represent. In actual investigations, you should always use a ruler when drawing tables by hand and include clear headings.

请注意，每个数值都清楚地标注了单位（米）。这避免了混淆，并确保任何阅读该表格的人都能准确理解数字的含义。在实际调查中，手绘表格时要始终使用直尺，并包含清晰的标题。

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3. Organising Data: Frequency Tables | 整理数据：频数表

Raw data can be difficult to interpret at a glance. Grouping the long jump distances into equal intervals creates a grouped frequency table, which summarises the distribution of performance. We will use class intervals of width 0.5 m, starting from 2.5 m.

原始数据很难一眼看出趋势。将跳远距离分成相等的区间可以创建一个分组频数表，从而汇总成绩的分布情况。我们将使用宽度为0.5米的组距，从2.5米开始。

For Team A, the frequency distribution is:

对于A组，频数分布如下：

Distance (m)	Tally	Frequency
2.5 – 2.9	I	1
3.0 – 3.4	III	3
3.5 – 3.9	I	1

For Team B, the grouped table shows a different pattern:

对于B组，分组表则显示了不同的模式：

Distance (m)	Tally	Frequency
2.5 – 2.9		0
3.0 – 3.4	III	3
3.5 – 3.9	II	2

Notice that Team B has no jump in the lowest interval but has two jumps in the highest interval. The grouped table immediately highlights that Team B tends to achieve longer jumps. This is the power of summarising data before calculating formal statistics.

请注意，B组在最低区间没有成绩，但在最高区间有两个成绩。分组表立刻突显出B组往往能跳出更远的距离。这就是在计算正式统计量之前先汇总数据的力量。

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4. Data Visualisation: Bar Charts and Pie Charts | 数据可视化：条形图和饼图

Visual representations make frequency distributions even clearer. For grouped discrete data like our long jump intervals, a bar chart is ideal. Each bar’s height represents the frequency of that class, and the bars are separated by gaps to show the categories are distinct.

可视化表示能让频数分布更加清晰。对于像我们跳远区间这样的分组离散数据，条形图是理想的选择。每个条形的高度代表该组的频数，条形之间留有间隙以表示各类别是独立的。

To draw a bar chart for Team A, label the horizontal axis ‘Distance (m)’ with the three intervals, and the vertical axis ‘Frequency’ numbered 0 to 3. Draw bars with heights 1, 3, and 1. Always give the chart a title, such as ‘Long Jump Results for Team A’. The same process can be repeated for Team B. The visual comparison would quickly reveal that Team B’s middle bar is taller than Team A’s, and Team B also has a bar in the highest interval.

要为A组绘制条形图，请将横轴标注为’距离（米）’并标出三个区间，纵轴标注为’频数’并标出0至3的刻度。画出高度分别为1、3和1的条形。务必为图表添加标题，例如’Team A长跳成绩’。B组可以重复同样的过程。视觉对比会很快揭示B组的中间条形比A组的高，而且B组在最高区间也有一个条形。

Alternatively, a pie chart can show the proportion of jumps in each category. For Team A, calculate the angle for each sector using the formula:

或者，饼图可以显示每个类别中的跳跃次数比例。对于A组，使用以下公式计算每个扇区的角度：

Sector Angle = (Frequency ÷ Total Frequency) × 360°

Team A total frequency = 5. So the angles are:

A组总频数 = 5。因此角度为：

• 2.5-2.9 m: (1 ÷ 5) × 360° = 72°

  2.5-2.9 m: (1 ÷ 5) × 360° = 72°

• 3.0-3.4 m: (3 ÷ 5) × 360° = 216°

  3.0-3.4 m: (3 ÷ 5) × 360° = 216°

• 3.5-3.9 m: (1 ÷ 5) × 360° = 72°

  3.5-3.9 m: (1 ÷ 5) × 360° = 72°

Using a protractor, you would then draw these sectors and label each with the category name or percentage. Both chart types are accepted in WJEC assessments, as long as they are neat and properly labelled.

然后使用量角器画出这些扇区，并标注每个扇区的类别名称或百分比。在WJEC考试中，只要整洁并正确标注，这两种图表类型都是被接受的。

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5. Central Tendency: Mean, Median, and Mode | 集中趋势：均值、中位数和众数

Now we move from visual displays to numerical summaries. The mean, median, and mode are three measures that describe the ‘centre’ of a data set. We will calculate them for the ungrouped long jump distances of Team A.

现在我们从可视化展示转向数值汇总。均值、中位数和众数是描述数据集’中心’的三种度量。我们将用A组未分组的跳远距离来计算它们。

First, list Team A’s distances in ascending order: 2.9, 3.1, 3.2, 3.4, 3.5.

首先，将A组的距离按升序排列：2.9, 3.1, 3.2, 3.4, 3.5。

Mean = (Sum of all values) ÷ (Number of values)

Sum = 2.9 + 3.1 + 3.2 + 3.4 + 3.5 = 16.1
Number of values = 5
Mean = 16.1 ÷ 5 = 3.22 m (rounded to two decimal places)

总和 = 2.9 + 3.1 + 3.2 + 3.4 + 3.5 = 16.1
数值个数 = 5
均值 = 16.1 ÷ 5 = 3.22 米（保留两位小数）

The median is the middle value when data are ordered. Since there are 5 values, the 3rd value is the median: 3.2 m.

中位数是数据排序后的中间值。因为有5个值，第3个值就是中位数：3.2米。

The mode is the most frequently occurring value. In Team A, each distance appears only once, so there is no mode. It is perfectly acceptable to state that the data set has no mode.

众数是出现频率最高的值。在A组中，每个距离只出现一次，因此没有众数。可以说该数据集没有众数，这是完全可以接受的。

For comparison, Team B’s distances (3.0, 3.2, 3.3, 3.6, 3.7) give: Mean = (18.8 ÷ 5) = 3.76 m; Median = 3.3 m; and again, no mode. This confirms that Team B’s average performance is higher.

作为比较，B组的距离（3.0, 3.2, 3.3, 3.6, 3.7）给出：均值 = (18.8 ÷ 5) = 3.76 米；中位数 = 3.3 米；同样没有众数。这证实了B组的平均成绩更高。

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6. Measuring Spread: The Range | 测量离散程度：范围

While averages give a typical value, they do not show how consistent the performances are. The range is a simple measure of spread: it is the difference between the largest and smallest values.

虽然平均数给出了典型的数值，但它们并不显示成绩的一致性如何。范围是一种简单的离散度量：它是最大值和最小值之间的差值。

Range = Largest value – Smallest value

For Team A: Largest = 3.5 m, Smallest =

Published by TutorHao | KS3 统计 Revision Series | aleveler.com

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