📚 Statistical Investigation Report: Framework and Model Answers for Year 8 CCEA | Year 8 CCEA 统计调查报告：框架与范文
In the Year 8 CCEA Statistics curriculum, you are expected to plan, carry out and write up a full statistical investigation. A well-structured report shows your ability to think like a data detective — from asking the right question to drawing evidence-based conclusions. This article provides a clear writing framework and a model answer to help you achieve high marks.
在 Year 8 CCEA 统计课程中，你需要规划、实施并撰写一份完整的统计调查报告。一份结构清晰的报告能够展示你像数据侦探一样思考的能力——从提出恰当的问题，到得出基于证据的结论。本文将提供一个明确的写作框架和一篇范文，帮助你获得高分。
1. The Statistical Investigation Cycle | 统计调查周期
Every statistical investigation follows a cycle. You start by identifying a problem or question, then plan how to collect data. After gathering your data, you organise and display it, analyse it using statistical measures, interpret your findings and finally evaluate the whole process.
每一项统计调查都遵循一个周期。你首先要确定一个问题或疑问，然后规划如何收集数据。在收集到数据之后，你要整理并展示数据，用统计量进行分析，解释你的发现，最后对整个过程的优缺点进行评价。
2. Asking the Right Question | 提出恰当的问题
A strong statistical question is specific, measurable and can be answered with data. Avoid questions that can be answered with a simple ‘yes’ or ‘no’. Good examples include: ‘How many hours of sleep do Year 8 students get on a school night?’ or ‘What is the most common type of snack eaten during break?’
一个好的统计问题是具体的、可度量的，并且能用数据回答。要避免那些可以用简单的“是”或“否”来回答的问题。好的例子包括：“Year 8 的学生在考试前一晚睡几个小时？”或者“休息时间最常吃的零食是什么种类？”
Once you have a question, write a hypothesis — a prediction of what you think the results will show. For example: ‘I predict that the most common snack will be crisps.’ or ‘I predict that the average sleep time will be between 8 and 9 hours.’ This gives your investigation a clear focus.
一旦你确定了问题，就要写一个假设——也就是你对结果会是什么样子的预测。例如：“我预测最常见的零食将是薯片。”或者“我预测平均睡眠时间会在 8 到 9 小时之间。”这会让你的调查有一个明确的焦点。
3. Planning Your Data Collection | 规划数据收集
Decide what type of data you need. Will you collect primary data (gathered yourself, e.g. through a survey or experiment) or secondary data (already published, e.g. from a website)? For Year 8 investigations, primary data is most common because you can control the gathering process.
决定你需要哪种类型的数据。你是收集一手数据（自己通过调查或实验收集），还是二手数据（已经发布的，比如来自网站的数据）？对于 Year 8 的调查来说，一手数据最为常见，因为你可以控制收集过程。
Plan your sample carefully. A random sample from your class or year group is often enough, but make sure it is unbiased. Decide exactly how many responses you need — a sample of 30 is often a good target for reliable averages. Write down your data collection sheet with clear categories or measurement units before you begin.
仔细规划你的样本。从你班级或年级组中进行随机抽样通常就足够了，但要确保样本没有偏差。明确你需要多少份回答——对于可靠的平均值来说，30 份样本通常是一个不错的目标。在开始之前，先用清晰的类别或度量单位写好你的数据收集表。
4. Gathering Data Reliably | 可靠地收集数据
When collecting data, be consistent and fair. Ask every person exactly the same question in the same way. If you are measuring, use the same instrument and read it carefully. Record your raw data neatly in a table with clear headings such as ‘Student’, ‘Hours of sleep’, or ‘Favourite snack’.
收集数据时，要保持一致和公平。用完全相同的方式向每个人提出完全相同的问题。如果你在测量，要使用相同的工具并仔细读数。将你的原始数据整齐地记录在一个表格中，表格要有清晰的标题，如“学生”、“睡眠小时数”或“最喜爱的零食”。
Always collect more data than you think you need, because you may later spot an error or an outlier that needs to be removed. An outlier is a value that is much higher or lower than the others and may need special attention.
收集的数据总要略多于你认为需要的量，因为你之后可能会发现需要删除的错误或异常值。异常值是指一个比其他值高很多或低很多的数值，可能需要特别关注。
5. Organising and Displaying Data | 整理和展示数据
Once you have your raw data, organise it into a frequency table. A tally chart can help you count how many times each value or category appears. Then you can create appropriate diagrams. For numerical data, use dot plots or stem-and-leaf diagrams; for categorical data, use bar charts or pictograms. Always label axes and give a title.
一旦你有了原始数据，就要把它整理成频数表。划记表可以帮助你数出每个值或类别出现的次数。然后你就可以制作合适的图表了。对于数值型数据，使用点状图或茎叶图；对于分类型数据，使用条形图或象形图。一定要给坐标轴加上标签并给出标题。
Your diagrams should make the data easier to understand at a glance. A good chart tells a story — you can already see which category is most popular or how spread out the data are.
你的图表应当让数据一目了然。一张好的图表能够讲述一个故事——你一眼就能看出哪个类别最受欢迎，或者数据分布有多广。
6. Analysing Data with Measures | 使用统计量分析数据
Use statistical measures to summarise your data. For numerical data, calculate the averages: mode (the most frequent value), median (the middle value when ordered) and mean. The mean is found by adding all values and dividing by the number of values.
Mean = Σx ÷ n
使用统计量来总结你的数据。对于数值型数据，计算各种平均数：众数（出现最频繁的值）、中位数（排序后位于中间的值）和平均数。平均数的计算方法是，将所有数值相加，再除以数值的个数。
平均数 = Σx ÷ n
Also calculate the range (largest value − smallest value) to describe the spread. For categorical data, the mode is the main average you can use. Always show your working clearly so the reader can follow your steps.
还要计算全距（最大值 − 最小值）来描述分散程度。对于分类型数据，众数是你可以使用的主要平均数。始终清晰地展示你的计算过程，这样读者才能跟上你的步骤。
7. Interpreting Results and Drawing Conclusions | 解释结果并得出结论
Look back at your hypothesis. Was your prediction correct? Use numbers from your analysis to support your conclusion. For example: ‘The mode was 8 hours, which supports my hypothesis that most students get between 8 and 9 hours of sleep. However, the range was 7 hours, showing a wide variation.’
回头看看你的假设。你的预测正确吗？用你分析中的数字来支持你的结论。例如：“众数为 8 小时，这支持了我的假设，即大多数学生的睡眠时间在 8 到 9 小时之间。然而，全距是 7 小时，显示出很大的差异。”
Do not just say ‘my hypothesis was right’ or ‘wrong’. Explain what the data actually tells you about the real world. Mention any patterns, unusual values or surprising findings you spotted when examining your charts.
不要仅仅说“我的假设是对的”或“错的”。要解释这些数据实际上告诉你关于现实世界的什么信息。提及你在查看图表时发现的任何模式、异常值或令人惊讶的结果。
8. Evaluating the Investigation | 评价调查过程
No investigation is perfect. In your evaluation, discuss what went well and what could be improved. Did you have a large enough sample? Was the question understood by everyone? Were there any sources of bias? If you removed an outlier, explain why and how it might have affected your mean.
没有哪项调查是完美的。在你的评价中，讨论哪些地方做得好，哪些地方可以改进。你的样本量足够大吗？每个人都理解你的问题吗？存在任何偏差来源吗？如果你去除了一个异常值，解释为什么这样做，以及它可能如何影响了你的平均值。
Finally, suggest how you would improve the investigation next time. For instance, you could collect data from more year groups, use a more precise measurement tool or ask a supplementary question to gain deeper insight.
最后，建议下次你将如何改进这项调查。例如，你可以从更多年级组收集数据，使用更精确的测量工具，或者问一个补充问题以获得更深入的见解。
9. Report Structure and Format | 报告结构与格式
Your final report should be clearly organised under the following headings. Use the table below as a checklist when writing your own investigation.
你的最终报告应该按照以下标题清晰地组织起来。在撰写自己的调查报告时，可以使用下表作为检查清单。
| Section (English) | 中文部分 | What to Include |
|---|---|---|
| Title and Hypothesis | 标题与假设 | Clear question and prediction |
| Plan | 计划 | Data type, sample size, collection method |
| Data Collection | 数据收集 | Raw data table and tally chart |
| Data Display | 数据展示 | Appropriate chart with labels |
| Analysis | 分析 | Averages, range, working shown |
| Conclusion | 结论 | Answer the question, refer to hypothesis |
| Evaluation | 评价 | Strengths, weaknesses and improvements |
10. Worked Example: Sleep Hours Survey | 范文示例：睡眠时间调查
Title and Hypothesis. The question I chose was ‘How many hours of sleep do Year 8 students in my class get on a school night?’ My hypothesis stated that most students would get between 8 and 9 hours of sleep, and that the mean would be around 8.5 hours.
标题与假设。 我选的问题是我班上 Year 8 的学生在一个上学日的晚上睡几个小时？我的假设是，大多数学生的睡眠时间会在 8 到 9 小时之间，平均时间大约会是 8.5 小时。
Plan. I decided to collect primary data by asking every student in my class of 30. I prepared a simple questionnaire with one clear question: ‘How many hours of sleep did you get last night?’ I recorded answers to the nearest half hour in a data collection table. I planned to draw a dot plot and calculate the mean, median, mode and range.
计划。 我决定通过问我班上 30 名同学中的每一个人来收集一手数据。我准备了一份简单的问卷，只包含一个清晰的问题：“你昨晚睡了多少小时？”我把答案记录到最接近的半小时，填入数据收集表中。我计划画一个点状图，并计算平均数、中位数、众数和全距。
Data Collection. I walked around the class during registration and asked each person. I recorded the following raw data (hours): 8, 7.5, 9, 8, 8.5, 9, 7, 10, 8, 8, 9, 8.5, 7.5, 8, 9.5, 8, 7, 10.5, 8, 8.5, 9, 9, 7.5, 8, 10, 8, 9, 7, 8.5, 9. I immediately spotted one unusually high value (10.5) but kept it for the time being.
数据收集。 我在早间报到的时候在班级里走动，询问了每一个人。我记录了以下原始数据（小时）：8, 7.5, 9, 8, 8.5, 9, 7, 10, 8, 8, 9, 8.5, 7.5, 8, 9.5, 8, 7, 10.5, 8, 8.5, 9, 9, 7.5, 8, 10, 8, 9, 7, 8.5, 9。我立刻发现了一个异常高的值（10.5），但暂时保留。
Organising Data. I created a frequency table using tally marks.
整理数据。 我使用划记制作了一个频数表。
| Sleep (h) | Tally | Frequency |
| 7 | ||| | 3 |
| 7.5 | ||| | 3 |
| 8 | |||| ||| | 8 |
| 8.5 | |||| | 4 |
| 9 | |||| || | 7 |
| 9.5 | | | 1 |
| 10 | || | 2 |
| 10.5 | | | 1 |
I then drew a dot plot on squared paper. The dots clustered strongly between 8 and 9 hours, with a clear gap at 10.5 hours. This suggested the 10.5 value might be an outlier.
接着我在方格纸上画了点状图。点状图强烈地聚集在 8 到 9 小时之间，在 10.5 小时处有一个明显的间隔。这暗示 10.5 这个值可能是一个异常值。
Analysis. First I calculated all averages with the full data set. Mode: 8 hours (appeared 8 times). The median: after ordering the 30 values, the 15th and 16th values were both 8.5, so median = 8.5 hours. Mean: I added the hours carefully: sum = 7×3 + 7.5×3 + 8×8 + 8.5×4 + 9×7 + 9.5×1 + 10×2 + 10.5×1 = 21 + 22.5 + 64 + 34 + 63 + 9.5 + 20 + 10.5 = 244.5. Then mean = Σx ÷ n = 244.5 ÷ 30 = 8.15 hours. Range = 10.5 − 7 = 3.5 hours.
分析。 首先我用完整的数据集计算了所有平均数。众数：8 小时（出现了 8 次）。中位数：将 30 个数值排序后，第 15 个和第 16 个值都是 8.5，所以中位数 = 8.5 小时。平均数：我仔细地将小时数相加：总和 = 7×3 + 7.5×3 + 8×8 + 8.5×4 + 9×7 + 9.5×1 + 10×2 + 10.5×1 = 21 + 22.5 + 64 + 34 + 63 + 9.5 + 20 + 10.5 = 244.5。然后平均数 = Σx ÷ n = 244.5 ÷ 30 = 8.15 小时。全距 = 10.5 − 7 = 3.5 小时。
The single value of 10.5 seemed too high compared with all the others. I decided to treat it as an outlier and recalculated the mean without it: new sum = 244.5 − 10.
Published by TutorHao | Year 8 统计 Revision Series | aleveler.com
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