📚 Year 9 WJEC Statistics: Essay Writing Framework and Model Answer | 九年级 WJEC 统计：论文写作框架与范文
Writing a statistical investigation essay for WJEC Year 9 requires a clear structure, careful planning and precise use of data. This guide will walk you through a complete framework, from forming a hypothesis to drawing conclusions, and provide a model answer so you can see exactly how to apply each step in your own work.
为 WJEC 九年级统计课程撰写调查论文需要清晰的结构、细致的规划以及准确的数据运用。本指南将带你走完一套完整的写作框架，从提出假设到得出结论，并附上一篇范文，让你直观地看到如何在自己的作业中应用每一步。
1. Understanding the Investigation Task | 理解调查任务
Every WJEC statistical essay begins with a real-world question or a prompt that asks you to explore a relationship, compare groups or estimate a population parameter. Reading the task carefully is the first step. You must identify whether you are being asked to describe, compare or predict.
每一篇 WJEC 统计论文都从一个真实世界的问题或提示开始，要求你探索某种关系、比较不同组别或估计总体参数。仔细阅读任务是第一步。你必须分辨出题目是要求你描述、比较还是预测。
Before you choose a topic, ask yourself three questions: Can I collect data for this easily? Does it involve both categorical and numerical variables? Is the scope narrow enough to handle within the word limit? Typical Year 9 topics include screen time vs sleep, revision hours vs test scores, or comparing reaction times between left- and right-handed students.
在选定主题之前，问自己三个问题：我能比较容易地收集到数据吗？它是否同时涉及分类变量和数值变量？范围是否足够窄，能在字数限制内完成？九年级常见的选题包括屏幕使用时间与睡眠的关系、复习时长与考试成绩，或者左手与右手学生的反应时间比较。
2. Forming a Hypothesis | 提出假设
A hypothesis is a testable statement that predicts what you expect to find. WJEC examiners expect you to write a null hypothesis (H₀) and an alternative hypothesis (H₁). Even at Year 9, using this format shows statistical thinking.
假设是一个可检验的陈述，用来预测你期望发现的结果。WJEC 考官希望你写出原假设 (H₀) 与备择假设 (H₁)。即使在九年级，使用这种格式也能体现统计思维。
For a correlation investigation, H₀ might be ‘There is no association between screen time and hours of sleep.’ H₁ would then be ‘There is a negative association between screen time and hours of sleep.’ Always define your variables clearly: ‘Screen time’ means daily hours spent on phones or tablets, and ‘Sleep’ means average hours per night during the school week.
对于相关性调查，H₀ 可以是“屏幕使用时间与睡眠时长之间没有关联”。H₁ 则是“屏幕使用时间与睡眠时长之间存在负相关”。始终清晰地定义你的变量：“屏幕使用时间”指每天花在手机或平板上的小时数，“睡眠”指上学日每晚的平均睡眠小时数。
You do not need to conduct a formal significance test in Year 9, but stating a hypothesis gives your essay direction and allows you to refer back to it in the conclusion.
在九年级你不需要进行正式的显著性检验，但陈述假设能为你的论文提供方向，并让你在结论中能够呼应假设。
3. Designing Data Collection | 设计数据收集方案
Decide how you will gather your data. A questionnaire, an observation sheet or a short experiment are all acceptable. The method must be ethical, repeatable and free from obvious bias. For example, if you are asking about screen time, design a simple table where participants can record their daily hours for a full week.
确定你将如何收集数据。问卷、观察记录表或简单实验都是可接受的方法。所用方法必须符合伦理、可重复且无明显偏倚。例如，如果你要询问屏幕使用时间，设计一个简单的表格，让参与者记录一整周的每日使用时长。
Pilot your data collection tool with two or three friends first. This helps you spot ambiguous questions. If someone asks, ‘Does streaming music count as screen time?’ you can clarify before the real data collection.
先用两三位朋友试测你的数据收集工具。这有助于发现含糊不清的问题。如果有人问“在线听歌算不算屏幕时间？”你就能在正式收集前予以澄清。
Always include a short paragraph in your essay justifying why you chose a particular method. For instance, ‘A questionnaire was used because it allows quick, anonymous collection of numerical data from many students during form time.’
务必在论文中加入一小段文字，说明你选择特定方法的理由。例如：“采用问卷是因为可以在晨会时间快速、匿名地从许多学生那里收集数值数据。”
4. Sampling Strategy | 抽样策略
Your sample should be described clearly. At Year 9, convenience sampling – such as asking 30 students from your year group – is usually acceptable, but you must acknowledge its limitations. Explain how you selected participants: ‘I distributed the questionnaire to every fifth person entering the canteen at break time.’
你的样本要描述清楚。在九年级，便利抽样——例如从你所在年级选取 30 名学生——通常是可以接受的，但你必须承认其局限性。说明你如何选择参与者：“我在课间休息时，向每第五个进入食堂的人发放问卷。”
Avoid using a sample that is too small; 25 to 40 individuals is a sensible range for a school-based investigation. If you want to aim higher, mention what a stratified or random sample would look like, and discuss why you could not use it due to time constraints.
避免样本过小；对于校内调查，25 到 40 人是较为合理的范围。如果你想更上一层，可以提及分层抽样或随机抽样会是什么样子，并说明因时间限制你未能采用的原因。
Record relevant demographic details, such as year group or gender, but never collect identifiable personal data. All your data sheets should use codes or numbers instead of real names.
记录相关的背景信息，如年级或性别，但绝不收集可识别的个人数据。你所有的数据表格都应用代码或编号代替真实姓名。
5. Organising Raw Data | 整理原始数据
Once you have your completed questionnaires, transfer the data into a structured table. This table should list each participant’s code in the first column, with subsequent columns for each variable. For a screen time study, you might have columns for ‘Participant’, ‘Daily Screen Time (hours)’, ‘Sleep (hours)’ and ‘Gender’.
一旦收回填好的问卷，就将数据转移到一个结构化的表格中。该表格应在第一列列出每位参与者的代码，随后各列对应每个变量。就屏幕时间研究而言，你可能会设置“参与者”、“每日屏幕时间（小时）”、“睡眠（小时）”和“性别”等列。
Check for obvious errors, sometimes called outliers at this stage. If someone reports sleeping two hours a night on a school day while also reporting five hours of screen time, go back and verify the response if possible. Document any data cleaning you do in your essay.
检查是否存在明显错误，此时通常称为异常值。如果有人报告在上学日每晚只睡两小时，同时又报告五小时屏幕时间，尽可能回去核实该回答。你在论文中要记录所进行的任何数据清洗。
Present the cleaned data in your essay either as a full table in the appendix or as a snippet in the main body with a summary. The exam board loves to see that you have been meticulous.
将清洗后的数据在正文中以摘要形式呈现，或作为完整表格放入附录。考试局非常看重你细致入微的态度。
6. Graphs and Charts | 图表展示
Graphs turn numbers into a story. At Year 9, you are expected to create at least two types of display: one for comparing groups, such as a dual bar chart or comparative box plot, and one for showing relationships, usually a scatter diagram.
图表能把数字变成故事。九年级要求你创建至少两种类型的展示图：一种用于比较组别，例如双条形图或并排箱线图；另一种用于展示关系，通常是散点图。
When drawing a scatter diagram, plot the independent variable on the x-axis. In a screen time vs sleep investigation, screen time is the independent variable, and sleep is the dependent variable. Add a line of best fit by eye, and use a ruler. Describe the correlation direction, strength and any unusual points.
绘制散点图时，将自变量标在 x 轴上。在屏幕时间与睡眠的调查中，屏幕时间是自变量，睡眠是因变量。用目测法添加一条最佳拟合线，并借助直尺。描述相关的方向、强度以及任何异常点。
Always label axes, give your chart a title and include a key if necessary. A good title is like a newspaper headline: ‘Scatter diagram showing a negative correlation between daily screen time and sleep for Year 9 students.’
始终给坐标轴加标签、为图表命名，并在需要时添加图例。好标题就像报纸标题：“显示九年级学生每日屏幕时间与睡眠之间负相关关系的散点图。”
If comparing boys and girls, you might produce side-by-side box plots for sleep hours. Calculate the five-number summary for each group—minimum, lower quartile, median, upper quartile, maximum—before you draw.
如果比较男生和女生，你可以为睡眠时长绘制并排箱线图。绘制前，先分别计算每一组的五数总结——最小值、下四分位数、中位数、上四分位数、最大值。
7. Summary Statistics | 汇总统计量
Numbers alone are not enough; you must calculate and interpret them. For each numerical variable, find the mean, median, mode and range. Also compute the interquartile range (IQR) if you are discussing spread in relation to outliers.
光有数字还不够；你必须计算并解读它们。对每一个数值变量，求出平均数、中位数、众数和极差。如果你要结合异常值讨论离散程度，还需计算四分位距 (IQR)。
Show your calculations step by step in the essay, even if you used a calculator. For the mean of sleep hours: sum all sleep values and divide by the number of students. Use the formula Mean = Σx / n in your method section.
在论文中逐步展示你的计算过程，即便你使用了计算器。对于睡眠时长的平均数：将所有睡眠值相加再除以学生人数。在方法部分使用公式 平均数 = Σx / n。
Interpret the statistics in context. For example: ‘The median sleep time was 7.5 hours, which means half the students slept less than this and half slept more. The IQR of 1.2 hours suggests a relatively consistent sleep pattern within the group.’ Never leave a statistic dangling without a sentence of meaning.
结合背景解读统计量。例如：“睡眠时间的中位数为 7.5 小时，这意味着半数学生睡眠少于此值，半数多于此值。四分位距为 1.2 小时，表明该组内睡眠模式较为一致。”绝不要让一个统计量孤立在那里，不给任何解释性句子。
8. Analysing and Linking to Hypothesis | 分析与关联假设
This is the heart of your essay. Bring together your graphs, statistics and original hypothesis. If your scatter plot shows a downward trend and the calculated mean sleep decreases as screen time categories increase, you have evidence to support H₁.
这是你论文的核心。将你的图表、统计量与原始假设结合起来。如果你的散点图呈现下降趋势，且计算出的平均睡眠时间随着屏幕时间类别的增加而减少，你便有了支持 H₁ 的证据。
Avoid writing ‘This proves my hypothesis is correct.’ Instead, use phrases like ‘The data suggests…’ or ‘There is some evidence to support the alternative hypothesis, but other factors such as homework load may also affect sleep.’
避免写“这证明了我的假设是正确的”。而要使用这样的表述：“数据表明……”或“有部分证据支持备择假设，但其他因素，如作业负担，也可能影响睡眠。”
Discuss any outliers and their possible impact. If one student had very low screen time but still slept only six hours, mention that removing this point would strengthen the negative correlation, but caution that you should keep it unless you have a valid reason to exclude it.
讨论任何异常值及其可能的影响。如果有一名学生屏幕使用时间很低，却仍然只睡六小时，说明剔除该点后负相关会更强，但你要谨慎行事，除非有正当理由，否则应保留该点。
Comparing subgroups adds depth. You might note that the correlation appeared stronger for girls than for boys, but with only 15 students in each group, you cannot be certain.
比较子组能增加深度。你或许会注意到，女生组的负相关似乎强于男生组，但由于每组只有 15 名学生，你还无法确定。
9. Evaluation and Limitations | 评价与局限性
Every investigation has weaknesses, and acknowledging them shows maturity. Common limitations include small sample size, reliance on self-reported data and the use of convenience sampling which may not represent the whole year group.
每项调查都有不足之处，承认它们能体现你的成熟度。常见的局限包括样本量小、依赖自报数据，以及使用便利抽样可能无法代表整个年级。
Suggest improvements: ‘In future, I would use a random sample of 50 students stratified by year group. I would also use a screen time tracking app to collect more accurate data instead of asking students to estimate.’
提出改进建议：“将来我会采用按年级分层的随机抽样，选取 50 名学生。我还会使用屏幕时间追踪应用来收集更精确的数据，而不是让学生估算。”
If possible, comment on how reliable you think your conclusion is. You can say: ‘Because the scatter diagram shows a moderate negative correlation and the IQRs do not overlap across high- and low-screen-time groups, I am fairly confident that increased screen time is associated with reduced sleep in this sample.’
如果可能，评论你认为自己的结论有多可靠。你可以说：“由于散点图显示出中等程度的负相关，且高屏幕时间组与低屏幕时间组的四分位距没有重叠，我相当有信心认为，在此样本中，屏幕时间增加与睡眠减少有关。”
10. Model Answer – Screen Time and Sleep Investigation | 范文示例 – 屏幕时间与睡眠调查
The following model essay demonstrates how to put the framework into practice. The essay has been split into sections, each presented in English first, then in Chinese, so you can follow the argument step by step.
以下范文展示了如何将框架付诸实践。该范文被分成若干部分，每部分先给出英文，再给出中文，以便你逐步理解论证过程。
Title and Hypothesis: ‘An investigation into the relationship between daily screen time and hours of sleep among Year 9 students.’ H₀: There is no association between screen time and sleep. H₁: There is a negative association between screen time and sleep.
标题与假设：“关于九年级学生每日屏幕使用时间与睡眠时长关系的调查。” H₀：屏幕时间与睡眠之间无关联。H₁：屏幕时间与睡眠之间存在负相关。
Method: A questionnaire was given to 30 Year 9 students during tutor time. Each student recorded their average daily screen time (hours) and average sleep per school night (hours) over the previous week. Participants were selected by asking every third volunteer from the tutor group list. All responses were anonymous.
方法：在导师时间向 30 名九年级学生发放问卷。每位学生记录前一周的日均屏幕时间（小时）和上学日平均睡眠时间（小时）。参与者按导师小组名单中每第三名志愿者选取。所有回答均为匿名。
Results (Data Summary): Mean screen time was 5.2 hours (range 2–9), and mean sleep was 7.3 hours (range 5.5–9). The median sleep was 7.4 hours with an IQR of 1.1 hours. A scatter diagram was drawn with a line of best fit sloping downwards, indicating a negative correlation.
结果（数据摘要）：平均屏幕时间为 5.2 小时（范围 2–9），平均睡眠为 7.3 小时（范围 5.5–9）。睡眠中位数为 7.4 小时，四分位距为 1.1 小时。绘制了散点图，最佳拟合线向下倾斜，表明负相关关系。
Analysis: The data suggest that as screen time increases, sleep tends to decrease. Students with screen time above 7 hours all slept less than 7 hours. One outlier (screen time 9 hours, sleep 6 hours) was noted but retained. The evidence supports H₁, but the sample is small and limited to one year group.
分析：数据表明，随着屏幕时间的增加，睡眠时长趋于减少。屏幕时间超过 7 小时的学生睡眠均少于 7 小时。注意到一个异常值（屏幕时间 9 小时，睡眠 6 小时）但予以保留。证据支持 H₁，但样本较小且仅限于一个年级。
Conclusion and Evaluation: There appears to be a negative association between screen time and sleep in this sample. The investigation could be improved by using a larger, random sample and by measuring screen time with an app rather than self-reports. Overall, the findings reinforce the importance of managing screen time for better sleep.
结论与评价：在此样本中，屏幕时间与睡眠之间似乎存在负相关。通过采用更大的随机样本，并使用应用而非自报方式来测量屏幕时间，可以改进这项调查。总体而言，该发现印证了管理屏幕时间对改善睡眠的重要性。
11. Common Mistakes to Avoid | 常见错误提醒
One frequent error is confusing the dependent and independent variables. In a sentence like ‘We are investigating how sleep affects screen time,’ the direction is wrong if your hypothesis is about screen time affecting sleep. Always think: which variable is causing the change?
一个常见错误是混淆因变量和自变量。像“我们正在调查睡眠如何影响屏幕时间”这样的句子，如果你的假设是关于屏幕时间影响睡眠，方向就错了。始终要思考：哪个变量导致了变化？
Another mistake is drawing a bar chart for paired numerical data that should be a scatter plot. Bar charts compare categories, not continuous relationships. If you plot screen time on the x-axis as a category, you hide the continuous nature of the data.
另一个错误是，对应该画散点图的成对数值数据却绘制了条形图。条形图用于比较类别，而非连续关系。如果你将屏幕时间作为类别标在 x 轴上，就掩盖了数据的连续性本质。
Avoid writing vague sentences like ‘The results were good.’ Instead, refer to specific values: ‘The median sleep time decreased from 8.2 hours in the low-screen group to 6.5 hours in the high-screen group.’
避免写“结果不错”之类含糊的句子。相反，要引用具体数值：“低屏幕时间组睡眠中位数从 8.2 小时降至高屏幕时间组的 6.5 小时。”
Finally, do not forget to label your axes with units and give your charts titles. A graph without a title is like a map without a key – it confuses the reader and costs marks.
最后，切勿忘记给坐标轴标注单位并给图表加上标题。没有标题的图表就像没有图例的地图——会让读者困惑并扣分。
12. Checklist Before Submission | 提交前的检查清单
| Check Item | Done? |
|---|---|
| Hypothesis stated clearly (H₀ and H₁) | ☐ |
| Method described and justified | ☐ |
| Raw data table included | ☐ |
| Two appropriate graphs with titles and labels | ☐ |
| Summary statistics calculated step by step | ☐ |
| Analysis links back to hypothesis | ☐ |
| Evaluation discusses limitations and improvements | ☐ |
Use this checklist to tick off each section before you hand in your essay. Meeting every point puts you in the top mark band for structure and statistical communication.
在提交论文前，用这份清单逐项核对。每满足一项，就能让你在结构和统计表达方面进入最高分数段。
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