📚 Year 7 WJEC Statistics: Essay Writing Framework and Model Answer | Year 7 WJEC 统计：论文写作框架与范文
Writing a statistical report is a core skill in Year 7 WJEC Statistics. It involves collecting data, presenting it clearly, calculating averages and drawing sensible conclusions. This article provides a step-by-step framework and a full model answer to help you master statistical writing.
撰写统计报告是 Year 7 WJEC 统计学的核心技能，涉及收集数据、清晰地展示数据、计算平均数并得出合理的结论。本文提供分步写作框架与一篇完整范文，帮助你掌握统计写作。
1. Understanding the Task | 理解任务要求
Before you start, read the investigation question carefully. Identify what you are being asked to investigate, whether you need to collect primary data or use secondary data, and what statistical measures are expected. In Year 7 WJEC, common tasks include surveys about student habits, comparing two sets of data or looking for patterns in everyday numbers.
开始前要仔细阅读探究问题。明确需要调查什么，是需要收集一手数据还是使用二手数据，以及期望你计算哪些统计量。Year 7 WJEC 常见任务包括关于学生习惯的问卷调查、比较两组数据或寻找日常数字中的模式。
Hypothesis: Most statistical reports start with a statement you aim to test, such as ‘Year 7 girls spend more time on homework than boys’.
假设：大多数统计报告以一个你想要检验的陈述开始，如“七年级女生做作业的时间比男生多”。
Plan the data type: Decide if your data will be discrete (counted, e.g. number of pets) or continuous (measured, e.g. height in cm). This affects how you group and display it.
规划数据类型：决定数据是离散的（可数，如宠物数量）还是连续的（测量值，如身高厘米），这会影响你如何分组与展示数据。
2. Planning Your Statistical Report | 规划统计报告
A well-organised report follows the same structure a scientist would use. Our framework has six main sections: Introduction, Methodology, Results (tables and graphs), Statistical Calculations, Analysis, and Conclusion & Evaluation. Use this skeleton to organise your ideas before you write.
一份组织良好的报告遵循科学家使用的结构。我们的框架有六个主要部分：引言、方法、结果（表格与图表）、统计计算、分析以及结论与评估。写作前用这个骨架来组织思路。
For the WJEC statistics paper, you will often be asked to write a short report. Even if the task is broken into parts, always present your work with clear headings and explanations. This shows you understand the statistical process.
在 WJEC 统计试卷中，你常被要求写一份简短报告。即使题目分成小题，也总要用清晰的标题和解释呈现你的工作，这显示你理解统计过程。
Make sure you include a brief plan of how you will collect data. For a survey, note the number of participants, how they were chosen (e.g. random sample of 30 Year 7 students) and the questions you will ask.
确保包含一份如何收集数据的简要计划。如果是问卷调查，注明参与者人数、选择方式（如随机抽取 30 名 7 年级学生）以及你将提出的问题。
3. Writing the Introduction | 撰写引言
The introduction sets the scene. Start with one or two sentences explaining the topic and why it is interesting. Then state your hypothesis clearly. Finally, give a quick preview of what your report will cover. Keep it short but meaningful.
引言设定背景。先用一两句话解释主题及其有趣之处，然后清晰地陈述你的假设。最后简要预览报告将涵盖的内容。保持简短但有意义。
Example opening: ‘Pocket money is an important part of Year 7 students’ lives. I wanted to find out if boys receive more money than girls. My hypothesis is that boys get slightly more weekly pocket money. This report will present my survey results, calculations and conclusions.’
范例开篇：“零花钱是七年级学生生活中的重要部分。我想了解男生是否比女生得到更多零花钱。我的假设是男生每周零花钱略多。本报告将呈现我的调查结果、计算和结论。”
Use the introduction to show you have thought about the purpose of the investigation. Never jump straight into raw numbers without explaining what you are trying to find out.
利用引言展示你思考过调查的目的。绝对不要不解释研究目标就直接列出原始数字。
4. Describing Your Methodology | 描述方法
The methodology section explains exactly how you gathered your data. This allows someone else to repeat your investigation. Include the type of data collected, the sample size, how participants were selected and the tools used (e.g. paper questionnaire or online form).
方法部分准确解释你是如何收集数据的，这让他人可以重复你的调查。需包括收集的数据类型、样本量、参与者如何选出以及使用的工具（如纸质问卷或在线表单）。
For Year 7 work, a simple description is enough: ‘I created a questionnaire with two questions: “How much pocket money do you get each week?” and “Are you a boy or a girl?” I handed it to 30 randomly chosen Year 7 students during break time and collected the completed sheets the same day.’
对 7 年级作业而言，简单描述即可：“我制作了一份有两个问题的问卷：‘你每周得到多少零花钱？’和‘你是男生还是女生？’。我在休息时间随机分发给 30 名 7 年级学生，并于当天收齐。”
Mention any steps you took to make the data reliable, such as checking for missing answers or making sure people did not fill it in twice. Also state that responses were anonymous.
提及为提高数据可靠性所采取的任何措施，如检查缺失答案或确保无人重复填写。还要说明回答是匿名的。
5. Presenting Data with Tables and Graphs | 用表格与图表展示数据
Raw data is messy. Use a frequency table to organise it. For continuous data, use grouped intervals. Every table must have a clear title and labelled columns. In your report, present the table first, then describe what it shows.
原始数据杂乱，可用频数表加以整理。对于连续数据，使用分组区间。每张表格必须有清晰的标题和栏目标签。在报告中先呈现表格，再描述其显示的内容。
Example table for a pocket money survey:
零花钱调查的示例表格：
| Pocket money (£) | Tally | Frequency |
|---|---|---|
| 0.00 – 1.99 | |||| | 4 |
| 2.00 – 3.99 | |||| || | 7 |
| 4.00 – 5.99 | |||| |||| | 9 |
From this table, I can see that the most common pocket money range is £4.00 – £5.99, with 9 students receiving this amount. The fewest students received £0.00 – £1.99.
从该表格可以看出，最常见的零花钱区间是 4.00–5.99 英镑，有 9 名学生收到这一数额。最少的区间是 0.00–1.99 英镑。
Graphs help readers see patterns instantly. In Year 7, you will normally draw a bar chart for discrete data or a histogram-style bar chart for grouped continuous data. Always label axes, give a title and use equal scales. For comparisons, a dual bar chart works well. Comment on what the graph reveals: highest bar, lowest bar, symmetry.
图表能帮助读者立刻看出模式。在 7 年级，你通常为离散数据绘制条形图，为分组连续数据绘制直方图式的条形图。始终标注坐标轴、添加标题并使用等距刻度。对比时，双条形图效果很好。评论图表揭示的信息：最高柱、最低柱、对称性。
6. Calculating Key Statistics | 计算关键统计量
Numbers tell the story behind the graph. For any data set, you should calculate at least three measures: the mean, the median, the mode and sometimes the range. These are called averages and measures of spread.
数字讲述图表背后的故事。对于任何数据集，你应至少计算三个量：平均数、中位数、众数，有时还有极差。这些被称为平均数和离散量数。
- Mean = sum of all values ÷ number of values. It is the balancing point but can be affected by outliers.
- 平均数 = 所有数值之和 ÷ 数据个数。它是平衡点，但易受异常值影响。
- Median = the middle value when data is ordered. Not affected by extreme scores.
- 中位数 = 数据排序后的中间值，不受极端值影响。
- Mode = the value that appears most often. Great for categorical data.
- 众数 = 出现次数最多的数值，特别适用于分类数据。
- Range = largest value – smallest value. Shows how spread out the data is.
- 极差 = 最大值 – 最小值，显示数据的分散程度。
For grouped data, we estimate the mean using the midpoint of each interval. Show your working clearly step by step. For instance, from the pocket money table above: midpoint of £2.00–3.99 is £3.00, multiply by frequency 7, and so on. Then sum and divide.
对于分组数据，我们使用每个区间的中点来估算平均数。要逐步清晰地展示计算过程。例如，根据上表：2.00–3.99 英镑区间的中点是 3.00 英镑，乘以频数 7，依此类推，然后求和并除以总数。
Calculations without words are confusing. Always write a short sentence with each statistic: ‘The mean weekly pocket money is £4.20, meaning that if the total money were shared equally, each student would receive £4.20.’
没有文字说明的计算会令人困惑。每一个统计量都要配以简短句子：“每周零花钱的平均数是 4.20 英镑，这意味着如果把总金额平分，每名学生将得到 4.20 英镑。”
7. Analysing and Interpreting Results | 分析与解读结果
Analysis connects your data to the original hypothesis. Start by looking at your calculated averages. For example, if the mean for boys is £4.50 and for girls is £3.80, this supports the hypothesis that boys receive more. But you must also mention the spread: if the range for girls is huge, the mean might be less reliable.
分析把你的数据与原假设联系起来。首先看计算出的平均数。例如，如果男生平均零花钱为 4.50 英镑，女生为 3.80 英镑，这支持男生获得更多的假设。但你还必须提及离散程度：如果女生的极差很大，平均数的可靠性可能较低。
Look for patterns, anomalies or surprising results. Were there any students with zero pocket money? Did anyone receive an unusual amount that pulled the mean up? Use phrases like ‘The data suggests that…’, ‘A possible reason for this is…’ or ‘This could be because…’.
寻找模式、异常或令人惊讶的结果。是否有学生零花钱为零？是否有人得到异常高的数额拉高了平均数？使用诸如“数据表明……”“一个可能的原因是……”或“这可能是因为……”等表述。
Always compare the mean, median and mode. If they are close, the data is fairly symmetrical. If the mean is much higher than the median, there is a positive skew caused by a few high values. In Year 7, you are not required to use the word skew officially, but you can say ‘the mean is pulled up by a few large numbers’.
始终比较平均数、中位数和众数。如果它们接近，数据相当对称。如果平均数远高于中位数，说明存在由少数高值引起的正偏态。在 7 年级，不强制使用“偏态”一词，但可以说“平均数被几个大数值拉高了”。
8. Writing Conclusions and Evaluations | 撰写结论与评估
Your conclusion must answer the hypothesis directly. Was your prediction correct? Summarise the key finding in one sentence, then back it up with the most important number. Example: ‘My hypothesis was correct: boys in Year 7 do receive more weekly pocket money on average. The mean for boys was £4.80 compared with £3.60 for girls.’
结论必须直接回应假设。你的预测正确吗？用一句话总结关键发现，然后用最重要的数据加以支撑。例如：“我的假设正确：七年级男生平均每周零花钱确实更多。男生平均为 4.80 英镑，女生为 3.60 英镑。”
Evaluation is about being honest. No investigation is perfect. Discuss what went well and what could be improved. For Year 7, think about sample size (was 30 students enough?), data collection method (did some students exaggerate?), and whether you could have asked a more precise question.
评估在于诚实。没有任何调查是完美的。讨论哪些方面做得好，哪些可以改进。对 7 年级学生来说，考虑样本量（30 名学生够吗？）、数据收集方法（是否有学生夸大？），以及能否提出更精确的问题。
Suggest how you could extend the investigation. For instance, you could survey students from different year groups or ask how they spend their money. This shows higher-order thinking and will impress your teacher.
提出如何拓展调查的建议。例如，可以调查不同年级的学生，或询问他们如何花零花钱。这展现高阶思维，会给老师留下深刻印象。
9. Full Model Answer: Pocket Money Investigation | 完整范文：零花钱调查
The following is a complete model answer for a Year 7 WJEC statistics report. Read it carefully and notice how each section follows the framework. The topic is: ‘Do boys get more weekly pocket money than girls?’
以下是一份面向 Year 7 WJEC 统计报告的完整范文。仔细阅读，留意各节如何遵循写作框架。主题是：“男生每周零花钱是否比女生多？”
Introduction
引言
Pocket money gives Year 7 students independence, but does the amount depend on gender? I hypothesised that boys receive slightly more weekly pocket money than girls. To test this, I surveyed 30 students from Year 7 at Greenwood School and compared the average amounts for boys and girls.
零花钱给予七年级学生独立性，但金额是否取决于性别？我假设男生每周零花钱比女生略多。为验证这一假设，我调查了格林伍德学校 30 名七年级学生，比较了男生和女生的平均金额。
Methodology
方法
I designed a short paper questionnaire asking: ‘How much pocket money did you receive last week (in £)?’ and ‘Are you male or female?’ I randomly selected 15 boys and 15 girls from the Year 7 register. The survey was completed anonymously during form time under my supervision, and all 30 forms were returned.
我设计了一份简短的纸质问卷，问题为：“上周你得到多少零花钱（英镑）？”和“你的性别是？”我从七年级名册中随机选取 15 名男生和 15 名女生。问卷在导师时间于本人监督下匿名完成，全部 30 份均已收回。
Results – Data Presentation
结果——数据呈现
I grouped the data into intervals of £2.00 and created a frequency table for both groups combined, then a dual bar chart to compare genders.
我将数据按 2.00 英镑的区间分组，为两组合并制作了频数表，随后用双条形图进行性别比较。
| Pocket money (£) | Boys frequency | Girls frequency |
|---|---|---|
| 0.00 – 1.99 | 2 | 5 |
| 2.00 – 3.99 | 4 | 6 |
| 4.00 – 5.99 | 6 | 3 |
| 6.00 – 7.99 | 2 | 1 |
| 8.00 – 9.99 | 1 | 0 |
The table shows that more girls than boys fall into the lowest pocket money band, while boys dominate the higher bands. The dual bar chart I drew (not shown here) made this difference very clear visually.
表格显示处于最低零花钱区间的女生比男生多，而男生在较高区间占主导。我绘制的双条形图（此处未展示）视觉上使这一差异非常明显。
Statistical Calculations
统计计算
I calculated the estimated mean, median and range for each gender. Using midpoints (1.00, 3.00, 5.00, 7.00, 9.00):
我计算了每种性别的估算平均数、中位数与极差。使用中点（1.00, 3.00, 5.00, 7.00, 9.00）：
Boys’ estimated mean = (2×1 + 4×3 + 6×5 + 2×7 + 1×9) ÷ 15 = (2+12+30+14+9) ÷ 15 = 67 ÷ 15 ≈ £4.47. Girls’ estimated mean = (5×1 + 6×3 + 3×5 + 1×7 + 0×9) ÷ 15 = (5+18+15+7+0) ÷ 15 = 45 ÷ 15 = £3.00. The median for boys is the 8th value in ordered raw data, which fell in the £4.00–5.99 band, around £5.00; for girls the median fell around £3.00. The range for boys was £9.50 – £0.50 = £9.00; for girls £7.20 – £0.00 = £7.20.
男生估算平均数 = (2×1 + 4×3 + 6×5 + 2×7 + 1×9) ÷ 15 = 67 ÷ 15 ≈ 4.47 英镑。女生估算平均数 = (5×1 + 6×3 + 3×5 + 1×7 + 0×9) ÷ 15 = 45 ÷ 15 = 3.00 英镑。男生的中位数是排序后第 8 个值，落在 4.00–5.99 区间约 5.00 英镑；女生的中位数落在约 3.00 英镑。男生极差 = 9.50 – 0.50 = 9.00 英镑；女生极差 = 7.20 – 0.00 = 7.20 英镑。
Analysis
分析
The data supports my hypothesis. Boys’ mean (£4.47) is higher than girls’ (£3.00) by £1.47. The median shows a similar gap. However, the boys’ range is larger, meaning there is greater variation in the boys’ pocket money, with one boy receiving £9.50 which pulled the mean upward slightly. The girls’ data is more consistent, with 11 out of 15 girls receiving between £0.00 and £3.99. The mode for both groups falls in the £4.00–5.99 band for boys and £2.00–3.99 for girls, underscoring the trend.
数据支持我的假设。男生平均数（4.47 英镑）比女生（3.00 英镑）高 1.47 英镑。中位数也显示相似差距。然而，男生极差更大，意味着男生零花钱的差异更大，其中一名男生收到 9.50 英镑，略微拉高了平均数。女生数据更为一致，15 名女生中有 11 名收到 0.00–3.99 英镑。两组的众数分别落在男生的 4.00–5.99 区间和女生的 2.00–3.99 区间，进一步突显这一趋势。
Conclusion and Evaluation
结论与评估
My hypothesis was correct: Year 7 boys at Greenwood School receive more weekly pocket money than girls on average. The investigation went well because the sample was random and all surveys were returned. However, using last week’s pocket money may not fully represent the usual amount, as some students might have had a special occasion. In the future, I would ask for a typical week and include a larger sample from other Year 7 classes to increase reliability. I could also explore whether pocket money is linked to household chores.
我的假设正确：格林伍德学校七年级男生平均每周零花钱比女生多。调查进展顺利，因为样本随机且所有问卷均已收回。然而，使用上周的零花钱可能无法完全代表通常的金额，因为有些学生可能遇上了特殊场合。将来我会询问通常一周的金额，并从其他七年级班级纳入更大样本以提高可靠性。我还可以探究零花钱是否与家务劳动有关。
This model answer demonstrates the full structure and connects every part to the original hypothesis. Use it as a template for your own reports.
这篇范文展示了完整的结构，并将每个部分都与原假设联系起来。可用作你自己报告的模板。
10. Common Mistakes to Avoid | 常见错误与避免方法
Even the best students slip up on these points. By being aware of them, you can pick up easy marks.
即使最优秀的学生也可能在这些点上失分。意识到这些问题，你就能轻松得分。
- Forgetting a title: Every table and graph needs a meaningful title. Without one, the reader does not know what the data represents.
- 忘记加标题：每张表格和图表都需要一个有意义的标题。没有标题，读者不知道数据代表什么。
- Confusing mean, median and mode: The mean uses all values; the median is the middle; the mode is the most frequent. Don’t mix them up.
- 混淆平均数、中位数与众数：平均数用到所有数值；中位数是中间值；众数是最频繁出现的值。别把它们搞混。
- Writing a conclusion without referring back to the hypothesis: Always answer the question you set out to investigate. A conclusion that simply says ‘The mean was 4.2’ is not enough.
- 写结论时没有回扣假设：始终回答你当初要探究的问题。只写“平均数是 4.2”的结论是不够的。
- Ignoring anomalies: If you spot an unusual value, mention it. Say how it affects the mean and what you might do about it if you redid the investigation.
- 忽略异常值：如果发现异常数值，要提到它。说明它如何影响平均数，以及如果重新调查你会如何处理。
- Not showing working: In calculations, always write the formula, the substitution and the final answer. Even if the final answer is wrong, you can get method marks.
- 不展示计算过程
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