📚 Year 10 Edexcel Statistics: Report Writing Framework & Sample Answers | 十年级爱德思统计：调查报告写作框架与范文
A well-structured statistical report demonstrates your ability to carry out an investigation, analyse data and communicate findings clearly. In the Edexcel Year 10 Statistics course, you may be asked to complete a controlled assessment or a project requiring a formal write-up. This article provides a step-by-step framework, key vocabulary and a full sample report to help you score top marks.
结构清晰的统计报告能展现你开展调查、分析数据并清晰传达结果的能力。在爱德思十年级统计课程中，你可能需要完成一项受控评估或项目，并提交正式的书面报告。本文将提供分步写作框架、关键学术用语以及一篇完整的范例报告，帮助你获得高分。
1. Understanding Statistical Report Writing | 认识统计报告写作
A statistical report is not just a list of numbers; it is a logical story guided by data. Your goal is to follow the statistical enquiry cycle, which includes defining a problem, planning data collection, gathering and processing data, performing calculations and creating graphs, and finally drawing conclusions and evaluating the process. Examiners expect clear structure, correct use of statistical terminology and evidence of critical thinking.
统计报告不仅仅是一串数字，而是一个以数据为导向的逻辑故事。你的目标是遵循统计调查周期，包括界定问题、规划数据收集、收集与处理数据、进行计算与绘图，最后得出结论并评估过程。考官期望结构清晰、正确使用统计术语，并体现出批判性思维。
2. The PPDAC Framework | PPDAC 框架
The PPDAC model (Problem, Plan, Data, Analysis, Conclusion) is widely used in statistics education. For Edexcel, adding an Evaluation stage (sometimes called the ‘Discussion’) is highly recommended. Therefore, your report can be structured as: Problem → Plan → Data → Analysis → Conclusion → Evaluation.
PPDAC 模型（问题、计划、数据、分析、结论）在统计教育中被广泛使用。对于爱德思考试，强烈建议附加一个“评估”环节（有时称为“讨论”）。因此，你的报告可以按照以下结构组织：问题 → 计划 → 数据 → 分析 → 结论 → 评估。
Problem – Clearly state the research question, the variables involved and the hypothesis you intend to test. The question should be specific, measurable and feasible within your context.
问题 – 清晰陈述研究问题、涉及的变量以及你计划检验的假设。问题应当具体、可测量且在自身情境中可行。
Plan – Describe your sampling method, data collection instrument and how you will ensure the data is reliable and unbiased. Justify your choices using statistical reasoning.
计划 – 描述你的抽样方法、数据收集工具，以及你将如何确保数据可靠、无偏。使用统计推理说明你的选择理由。
Data – Present raw data in well-labelled tables. Include summary statistics such as totals, means or frequencies. Mention any cleaning steps, such as removing outliers or handling missing values.
数据 – 在标注清晰的表格中呈现原始数据。包含总计、均值或频数等汇总统计量。提及任何清洗步骤，如剔除异常值或处理缺失值。
Analysis – Perform appropriate calculations and create graphs (e.g. scatter graphs, box plots, bar charts). Compute measures of central tendency and spread, correlation coefficients or other relevant statistics. Interpret what the numbers and graphs show.
分析 – 进行恰当的计算并创建图表（例如散点图、箱线图、条形图）。计算集中趋势和离散程度的度量、相关系数或其他相关统计量。解读数字和图表所显示的信息。
Conclusion – Answer the original question, refer back to the hypothesis and support your findings with statistical evidence. Avoid overgeneralising – acknowledge that the results apply to your sample.
结论 – 回答最初的问题，回顾假设并用统计证据支持你的发现。避免过度概括——承认结果仅适用于你的样本。
Evaluation – Critically examine limitations of your method, such as sample size, bias or confounding variables. Suggest realistic improvements for future investigations.
评估 – 批判性地审视你的方法的局限性，例如样本量、偏差或混杂变量。为未来的调查提出切实可行的改进建议。
3. Problem – Stating the Question and Hypothesis | 问题——提出研究问题与假设
A strong report begins with a precise, testable question. Avoid vague wording like “Does social media affect sleep?” Instead, write “Is there a relationship between the daily hours spent on social media and hours of sleep among Year 10 students?” Identify the independent variable (e.g. social media hours) and the dependent variable (e.g. sleep hours). Then formulate a null hypothesis (H₀) and an alternative hypothesis (H₁). For a correlation study, you might use: H₀: There is no correlation between social media time and sleep duration. H₁: There is a correlation between social media time and sleep duration. Using statistical notation can boost marks, e.g. H₀: ρ = 0, H₁: ρ ≠ 0, where ρ represents the population correlation coefficient.
一份有力的报告始于一个精确、可检验的问题。避免诸如“社交媒体会影响睡眠吗？”这样模糊的措辞。相反，应写为“十年级学生每日使用社交媒体的时长与睡眠小时数之间是否存在关系？”确定自变量（如社交媒体时长）和因变量（如睡眠时长）。然后构造零假设(H₀)和备择假设(H₁)。对于相关性研究，你可以这样写：H₀: 社交媒体时间与睡眠时长之间无相关关系。H₁: 社交媒体时间与睡眠时长之间存在相关关系。使用统计符号可以增加分数，例如 H₀: ρ = 0，H₁: ρ ≠ 0，其中 ρ 代表总体相关系数。
4. Plan – Sampling and Data Collection | 计划——抽样与数据收集
Your planning section should explain how you obtained the data. Describe the target population (e.g. all Year 10 students in your school) and the sampling method. Common methods include simple random sampling, stratified sampling or systematic sampling. For example, “A stratified sample of 30 students was selected, with strata based on gender to maintain the same proportion as in the year group. Within each stratum, individuals were chosen using a random number generator.” Justify why this method reduces bias and makes the sample more representative. Also describe your data collection tool – a questionnaire, an experiment or secondary data from a reliable source. Mention steps taken to ensure confidentiality and honest responses.
你的计划部分应解释你是如何获得数据的。描述目标总体（例如你所在学校的所有十年级学生）和抽样方法。常见方法包括简单随机抽样、分层抽样或系统抽样。例如，“采用分层抽样选取了30名学生，以性别作为分层依据，以保持与年级组相同的比例。在每个层内，使用随机数生成器选择个体。”说明为什么该方法能减少偏差并使样本更具代表性。同时描述你的数据收集工具——问卷、实验或来自可靠来源的二手数据。提及其他为确保保密性和真实回答而采取的步骤。
5. Data – Presenting Raw Data and Summary Tables | 数据——呈现原始数据和汇总表
Start with a clearly labelled table of raw data. Each column should have a heading with units. Below is an example table for a study on revision hours and test marks.
从一张标注清晰的原始数据表开始。每一列都应有带单位的标题。以下是一份关于复习时间与考试成绩研究的示例表格。
| Student | Revision (hours) | Test score (%) |
|---|---|---|
| A | 5 | 62 |
| B | 2 | 41 |
| C | 8 | 89 |
| D | 3 | 48 |
| E | 6 | 75 |
After presenting the raw data, calculate summary statistics like the mean, median and range. For the revision hours above: Mean = (5+2+8+3+6) ÷ 5 = 4.8 hours; Median = 5 hours; Range = 6 hours. Always show your working steps. Mention any data cleaning, for instance if you checked for impossible values or outliers, and explain your decisions.
呈现原始数据后，计算均值、中位数和极差等汇总统计量。就上述复习时间而言：均值 = (5+2+8+3+6) ÷ 5 = 4.8 小时；中位数 = 5 小时；极差 = 6 小时。始终展示你的计算步骤。提及任何数据清洗工作，例如你是否检查了不可能的值或异常值，并解释你的决定。
6. Analysis – Graphs and Descriptive Statistics | 分析——图表与描述统计
Visual representations make patterns clear. For a single variable, use a bar chart or a box plot. For bivariate data, a scatter graph is essential. Describe the shape, direction and strength of any relationship you observe. Calculate suitable averages and measures of spread: for symmetric data use the mean and standard deviation; for skewed data use the median and interquartile range (IQR). Remember to state the units and label axes correctly.
图形能让规律一目了然。对于单变量数据，使用条形图或箱线图。对于双变量数据，散点图必不可少。描述你观察到的任何关系的形状、方向和强度。计算合适的平均数和离散程度度量：对于对称数据，使用均值和标准差；对于偏斜数据，使用中位数和四分位距（IQR）。记住标出单位并正确标记坐标轴。
For the revision data, you could draw a scatter graph with ‘Revision hours’ on the x-axis and ‘Test score’ on the y-axis. The points suggest a positive correlation. Then compute the median test score (62%) and the IQR: Q₁ = 44.5%, Q₃ = 82%, so IQR = 37.5%. This tells us the middle 50% of scores span 37.5 percentage points.
对于复习数据，你可以绘制以“复习小时数”为x轴、“考试成绩”为y轴的散点图。这些点表明存在正相关。然后计算考试成绩的中位数（62%）和四分位距：Q₁ = 44.5%，Q₃ = 82%，因此 IQR = 37.5%。这告诉我们中间50%的分数跨度为37.5个百分点。
7. Analysis – Correlation and Relationships | 分析——相关性与关系
When investigating relationships between two variables, you must quantify the correlation. Edexcel Year 10 often expects Spearman’s rank correlation coefficient (rₛ). Spearman’s rank works with ranked data and does not require a linear relationship. The formula is rₛ = 1 – (6 Σ d²) / (n(n² – 1)), where d is the difference between the ranks of each pair, and n is the number of data pairs. A value of +1 indicates perfect positive correlation, -1 indicates perfect negative correlation, and 0 suggests no correlation.
在研究两个变量之间的关系时，你必须量化其相关性。爱德思十年级课程通常要求掌握斯皮尔曼等级相关系数（rₛ）。斯皮尔曼等级相关系数使用排序数据，且不要求线性关系。其公式为 rₛ = 1 – (6 Σ d²) / (n(n² – 1))，其中 d 为每对数据秩次的差值，n 为数据对的个数。值为 +1 表示完全正相关，-1 表示完全负相关，0 则表示没有相关性。
Let’s work through an example using the study time (hours) and test score (%) data from the sample report later. After ranking both variables, we calculate d and d². Suppose Σd² = 2.5 and n = 10, then rₛ = 1 – (6 × 2.5) / (10 × (100 – 1)) = 1 – 15 / 990 ≈ 0.985. This very high positive value indicates a strong tendency for students who study longer to achieve higher scores. Always interpret the coefficient in words, linking back to your hypothesis.
让我们用下文中范例报告里的学习时间（小时）与考试成绩（%）数据来演练一下。在对两个变量进行排序后，我们计算 d 和 d²。假设 Σd² = 2.5，n = 10，那么 rₛ = 1 – (6 × 2.5) / (10 × (100 – 1)) = 1 – 15 / 990 ≈ 0.985。这个非常高的正值表明，学习时间较长的学生有很强的趋势获得更高的分数。始终用文字解读系数，并联系回你的假设。
8. Conclusion – Interpreting Findings | 结论——解读结果
Your conclusion must directly answer the research question. Do not just restate the correlation coefficient; explain what it means in the context of your investigation. For example: “The Spearman’s rank coefficient of 0.985 shows a very strong positive correlation between revision time and test score. This supports the alternative hypothesis that a relationship exists. However, correlation does not imply causation – we cannot claim that longer revision causes higher scores without considering other factors such as prior ability.”
你的结论必须直接回答研究问题。不要仅仅重复相关系数；要解释它在你所研究情境中的含义。例如：“斯皮尔曼等级系数0.985表明复习时间与考试成绩之间存在非常强的正相关。这支持了存在相关关系的备择假设。然而，相关并不意味着因果——我们不能在不考虑先前能力等其他因素的情况下，断言更长的复习时间会导致更高的分数。”
Also state whether the findings are statistically significant if you have performed a hypothesis test, but at Year 10 this may be optional. Relate your result back to the population you sampled from, but be cautious: “These results suggest that among Year 10 students in our school, there is a link, but we cannot be certain this applies to all schools.”
如果你进行了假设检验，还要说明结果是否具有统计显著性，但在十年级，这部分可能是选做的。将你的结果联系回你所抽样的总体，但要保持谨慎：“这些结果提示，在我们学校的十年级学生中存在这种关联，但我们无法确定这适用于所有学校。”
9. Evaluation – Limitations and Improvements | 评估——局限性与改进
No investigation is perfect. A good report identifies weaknesses honestly and suggests sensible improvements. Common limitations include small sample size, convenience sampling (e.g. only using your class), self-reported data that may be inaccurate, and uncontrolled variables like stress or teaching quality. For our revision study, a limitation could be “The sample size of only 10 students may not represent the whole year group, and revision hours were self-reported, which might be overestimated.”
没有一项调查是完美的。一份好的报告会诚实地指出不足之处，并提出合理的改进建议。常见的局限包括样本量小、便利抽样（例如仅使用自己班级）、自我报告的数据可能不准确，以及无法控制的变量如压力或教学质量。对于我们复习情况的研究，一个局限可以是“仅10名学生的样本量可能无法代表整个年级，而且复习时间是自我报告的，可能被高估。”
Improvements: “In future, a larger stratified sample across multiple classes could be used. Revision time could be logged daily via an app
Published by TutorHao | Year 10 统计 Revision Series | aleveler.com
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