📚 Year 8 CCEA Statistics: Case Study Practical Exercises | Year 8 CCEA 统计：案例分析实战演练
Statistics is not just about numbers and formulas – it is a powerful tool for making sense of the world around us. In Year 8 CCEA Statistics, case studies bring data to life, showing how surveys, experiments and everyday observations can be turned into evidence-based conclusions. This article takes you through two complete practical exercises, step by step, so you can master data collection, presentation, analysis and interpretation. Whether you are preparing for an assessment or simply enjoy finding patterns in information, these real-world examples will build your confidence and skills.
统计学不仅仅是数字和公式——它是帮助我们理解周围世界的强大工具。在 Year 8 CCEA 统计课程中，案例分析将数据变得生动，展示了如何将调查、实验和日常观察转化为有依据的结论。本文将通过两个完整的实战演练，一步步带你掌握数据收集、呈现、分析和解读。无论你是在为考试做准备，还是单纯喜欢从信息中发现规律，这些真实世界的例子都会帮助你建立信心、提升技能。
1. What Is a Statistical Case Study? | 什么是统计案例分析？
A statistical case study is an in-depth investigation that uses data to answer a specific question or explore a real-life situation. Instead of just calculating mean or drawing one graph, you follow the entire statistical cycle: pose a question, gather data, organise and display it, analyse patterns, and draw a conclusion. In CCEA Year 8, you will often be asked to plan a simple survey or experiment, collect small sets of data, and present your findings clearly.
统计案例分析是一种深入调查，利用数据回答特定问题或探索真实场景。你不仅仅是计算平均数或画一张图表，而是遵循完整的统计周期：提出问题、收集数据、整理并展示数据、分析规律，最后得出结论。在 CCEA Year 8 课程中，你会经常被要求设计简单的调查或实验，收集小规模数据集，并清晰地呈现你的发现。
2. Case Study 1: Class Pet Survey | 案例一：班级宠物调查
Our first case study investigates the types and numbers of pets owned by students in a Year 8 class. The question we want to answer is: “What is the most common pet among pupils in 8A, and how many pets does a typical student have?” This is a straightforward survey that yields categorical and numerical data, perfect for practising frequency tables, bar charts and measures of central tendency.
我们的第一个案例研究调查的是 Year 8 班级中学生饲养宠物的种类和数量。我们要回答的问题是：“8A 班学生中最常见的宠物是什么？一个典型学生拥有多少只宠物？”这是一个简单的调查，能产生分类数据和数值数据，非常适合练习频数表、条形图以及集中趋势的度量。
3. Designing the Survey and Collecting Data | 设计调查并收集数据
We prepared a short questionnaire asking each pupil: “Do you have any pets? If yes, what type(s) and how many of each?” The responses were recorded on a tally sheet during form time. A total of 28 students took part. To keep the data manageable, we limited pet types to dog, cat, fish, bird, hamster, other, and none. Each student could list more than one type.
我们准备了一份简短的问卷，询问每位学生：“你有宠物吗？如果有，是什么种类？每种有多少只？”在早会时间用计数表记录回答。共有 28 名学生参与。为了让数据易于处理，我们把宠物种类限定为狗、猫、鱼、鸟、仓鼠、其他和无。每位学生可以列出多种答案。
4. Organising Raw Data into Frequency Tables | 将原始数据整理成频数表
To make sense of the raw results, we created a frequency table for pet types. Tally marks were counted and converted to numbers. For example: Dog 10, Cat 7, Fish 5, Bird 3, Hamster 4, Other 2, None 4. Notice that the total number of responses (35) is larger than the number of students (28) because some had more than one type of pet. For the number of pets per student, we made a separate frequency table: 0 pets → 4 students, 1 pet → 12, 2 pets → 7, 3 pets → 3, 4 pets → 2.
为了理清原始结果，我们为宠物种类制作了频数表。计数符号被转换成数字。例如：狗 10、猫 7、鱼 5、鸟 3、仓鼠 4、其他 2、无 4。注意总回答次数（35）大于学生人数（28），因为有些学生拥有超过一种宠物。关于每位学生拥有的宠物数量，我们制作了另一个频数表：0 只 → 4 人，1 只 → 12 人，2 只 → 7 人，3 只 → 3 人，4 只 → 2 人。
5. Displaying Data with Bar Charts and Pictograms | 用条形图和象形图展示数据
A vertical bar chart was drawn to show pet types, with the category on the horizontal axis and frequency on the vertical axis. The bars were coloured and labelled, and the chart had a clear title: “Pets Owned by 8A Students”. For the number of pets, we used a pictogram where one symbol (a paw print) represented one student. This made it easy to see that 12 students have exactly one pet – the most common amount. Both displays were neat, used a ruler, and had equal spacing.
我们绘制了一张垂直条形图来展示宠物种类，横轴是类别，纵轴是频数。条形图上色并加了标签，图表有清晰的标题：“8A 班学生拥有的宠物”。对于宠物数量，我们使用了象形图，一个符号（一个爪印）代表一名学生。这样很容易看出 12 名学生拥有正好一只宠物——这是最常见的数量。两个展示都整洁、用尺规作图，并且间隔相等。
6. Measures of Central Tendency: Mean, Median, Mode | 集中趋势度量：平均数、中位数、众数
From the frequency table of number of pets, we calculated the mode (most frequent value) as 1 pet, because 12 students fall into this group. The median was found by listing all 28 students’ pet counts in order: the 14th and 15th values are both 1, so median = 1. For the mean, we multiplied each pet count by its frequency, added the products (0×4 + 1×12 + 2×7 + 3×3 + 4×2 = 0+12+14+9+8 = 43) and divided by 28:
Mean = 43 ÷ 28 ≈ 1.54 pets
从宠物数量的频数表中，我们计算出众数（出现最多的值）是 1 只，因为有 12 名学生落在这个组。要找到中位数，我们把所有 28 名学生拥有的宠物数量从小到大排列：第 14 和第 15 个值都是 1，所以中位数 = 1。要计算平均数，我们把每个宠物数量值乘以对应的频数，将乘积相加（0×4 + 1×12 + 2×7 + 3×3 + 4×2 = 0+12+14+9+8 = 43），然后除以 28：
平均数 = 43 ÷ 28 ≈ 1.54 只
7. Range and Interpreting the Spread | 极差与数据分布的解读
The range is the difference between the highest and lowest values. In our case, the maximum number of pets is 4, the minimum is 0, so the range = 4 − 0 = 4. This tells us that pet ownership varies quite a bit within the class. Together with the mean (1.54) and mode (1), we can say a typical Year 8 student has about 1 or 2 pets, but a few pupils have more, pulling the mean slightly upwards.
极差是最大值与最小值的差。在我们的数据中，宠物数量的最大值是 4，最小值是 0，所以极差 = 4 − 0 = 4。这说明班级里宠物拥有情况差异较大。结合平均数（1.54）和众数（1），我们可以说，典型的 Year 8 学生大约有 1 到 2 只宠物，但有少数学生拥有更多，使得平均数略微偏高。
8. Case Study 2: Daily Step Count Challenge | 案例二：每日步数挑战
For the second case study, we moved from a survey to an experiment: tracking the daily step counts of five volunteers over one school week. The question was: “Do Year 8 pupils walk more on days they have PE lessons?” This introduces time-series data, line graphs, and comparisons between two sets of conditions. Steps were recorded using smartphone pedometers or school-provided counters.
第二个案例研究，我们从调查转向了实验：追踪五名志愿者在一周上学期间的每日步数。要回答的问题是：“Year 8 学生在有体育课的日子是不是走的路更多？”这引入了时间序列数据、折线图以及两组条件之间的比较。步数通过智能手机计步器或学校提供的计数器记录。
9. Recording Data in a Structured Table | 用结构化表格记录数据
We designed a data table with columns for the day of the week, whether it was a PE day (Yes/No), and the step count for each volunteer, plus an average step count for that day. The table made it easy to compare. For example, Monday (PE, Yes): 6500, 7200, 6100, 5800, 7000 → average 6520 steps. Wednesday (No PE): 4200, 4500, 3900, 4100, 3800 → average 4100 steps. The full five-day table allowed us to see patterns at a glance.
我们设计了一张数据表，列分别是一周中的星期几、是否有体育课（是/否）、每位志愿者的步数，以及当天的平均步数。表格使比较变得容易。例如，星期一（有体育课）：6500、7200、6100、5800、7000 → 平均 6520 步。星期三（无体育课）：4200、4500、3900、4100、3800 → 平均 4100 步。完整的五天数据表让我们一眼就能看出规律。
10. Drawing and Interpreting Line Graphs | 绘制并解读折线图
We created a double line graph: one line for the average steps on PE days (marked with a circle) and another line for non-PE days (marked with a square). The horizontal axis showed the day of the week, and the vertical axis showed steps from 0 to 8000. The lines clearly showed a peak on PE days. The graph also included a key, a title, and evenly spaced intervals. From the visual, we could see that step counts rose sharply on Monday and Thursday (both PE days) and dipped midweek.
我们制作了一张双折线图：一条折线表示有体育课日的平均步数（用圆圈标记），另一条表示无体育课日的平均步数（用方块标记）。横轴为星期，纵轴为步数，范围从 0 到 8000。两条折线清楚地显示有体育课日出现峰值。图表还包括图例、标题和等距刻度。从视觉上可以看出，步数在星期一和星期四（都是体育课日）急剧上升，在周中下降。
11. Comparing Two Data Sets Using Averages and Range | 用平均数和极差比较两组数据
We separated all daily step counts into two groups: PE days (Mondays and Thursdays) and non-PE days (Tuesdays, Wednesdays, Fridays). For PE days, the mean step count was approximately 6410, with a range of 5800 to 7200 → range = 1400. For non-PE days, the mean was about 4030, with a range from 3800 to 4500 → range = 700. This shows that not only do pupils walk more on PE days, but their activity levels are also more varied; on non-PE days, steps are lower and more consistent.
我们将所有每日步数数据分成两组：体育课日（周一和周四）与非体育课日（周二、周三、周五）。体育课日的平均步数约为 6410，极差从 5800 到 7200 → 极差 = 1400。非体育课日的平均步数约为 4030，极差从 3800 到 4500 → 极差 = 700。这表明，学生在体育课日不仅走路更多，而且活动水平的波动也更大；而在非体育课日，步数较低，也更稳定。
12. Drawing Conclusions and Evaluating the Case Study | 得出结论并评估案例研究
From the step data, we can conclude that Year 8 pupils do walk significantly more on days with PE lessons – the average step count was over 2000 steps higher. However, we must evaluate the study: the sample size was small (only five volunteers), and step counters might not be perfectly accurate. Also, weather or after-school clubs could affect results. A better design might include more students over several weeks. Despite these limitations, the case study successfully demonstrated the statistical process from question to evidence-based conclusion.
从步数数据中，我们可以得出结论：Year 8 学生在有体育课的日子确实走路明显更多——平均步数高出超过 2000 步。然而，我们必须评估这项研究：样本量较小（只有五名志愿者），计步器可能不完全准确。此外，天气或课后俱乐部也可能影响结果。更完善的设计可以包括更多学生并持续几周。尽管存在这些局限，该案例研究成功展示了从提出问题到基于证据得出结论的完整统计过程。
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