📚 How to Structure a Statistical Investigation Report: Framework and Model Answer | 统计调查论文写作框架与范文
In the CCEA IGCSE Statistics course, a high-scoring written report is not just a collection of calculations. It must follow the statistical enquiry cycle: plan, collect, process, discuss, and evaluate. This article explains a clear writing framework and provides a model extract so you can see how to turn raw data into convincing evidence.
在 CCEA IGCSE 统计课程中，高分书面报告不只是罗列计算。它必须遵循统计探究循环：计划、收集、处理、讨论和评价。本文讲解清晰的写作框架并提供范文节选，帮助你学会如何把原始数据转化为有说服力的证据。
1. Understanding the CCEA Statistics Report | 理解 CCEA 统计报告要求
The CCEA Statistics paper rewards structure, accuracy, and interpretation. Examiners look for a clear aim, a justified sampling method, suitable charts, correct calculations, and a conclusion that links back to the hypothesis.
CCEA 统计考试评分看重结构、准确性和解释。考官希望看到清晰的目标、合理的抽样方法、合适的图表、正确的计算，以及回到假设的结论。
A report usually contains these sections: introduction and hypothesis, method, data presentation, analysis, conclusion, and evaluation. Each section should flow logically into the next, and no chart or table should appear without being explained in words.
报告通常包含以下部分：引言与假设、方法、数据展示、分析、结论与评价。每个部分都应自然衔接，任何图表或表格出现时都必须有文字解释。
Examiners also check whether you use statistical vocabulary precisely, such as “sample”, “population”, “mean”, “range”, “outlier”, and “correlation”.
考官还会检查你是否准确使用统计术语，例如 “样本”、”总体”、”平均数”、”极差”、”异常值” 和 “相关性”。
2. Choosing a Hypothesis and Variables | 选择假设与变量
A strong hypothesis is specific, measurable, and comparative. For example: “Year 11 boys in our school tend to have a larger handspan than Year 11 girls.” Avoid vague statements such as “height affects performance.”
好的假设必须具体、可测量、可比较。例如：”我校 11 年级男生的手掌跨度往往大于女生。” 避免使用 “身高影响表现” 这类模糊表述。
Define your independent variable and dependent variable. In the example, gender is the independent variable and handspan is the dependent variable. This clarity helps you choose the right charts and statistics later.
明确自变量和因变量。在上述例子中，性别是自变量，手掌跨度是因变量。这种清晰性有助于你在后续选择合适的图表和统计量。
You can also state a null hypothesis and an alternative hypothesis. The alternative hypothesis is what you expect to find, while the null hypothesis usually states that there is no difference or no relationship.
你还可以写出原假设与备择假设。备择假设是你预期发现的结论，而原假设通常说明没有差异或没有关系。
3. Sampling and Data Collection Methods | 抽样与数据收集方法
You should describe how the sample was selected. A simple random sample reduces bias, while an opportunity sample is quicker but may not represent the whole year group.
你需要说明样本是如何选取的。简单随机样本可减少偏差，而机会样本更快，但可能无法代表整个年级。
Always give the sample size and explain why it is manageable. For IGCSE coursework, 30 to 60 participants are usually sufficient. A larger sample generally gives more reliable results, but it also takes more time to collect and process.
务必给出样本量并说明为何可行。在 IGCSE 课程作业中，30 至 60 名参与者通常足够。样本越大，结果通常越可靠，但收集和处理数据也需要更多时间。
Mention ethics: “All participants gave consent and data were anonymised.” This shows good practice and is often expected in a statistical enquiry.
提及伦理问题：”所有参与者均同意，且数据已匿名处理。” 这体现了良好实践，统计分析中也经常要求这一点。
4. Data Presentation Techniques | 数据展示方法
Choose charts that suit the data type. For comparing two distributions, use back-to-back stem-and-leaf diagrams or box plots. For categorical data, use bar charts or pie charts. For bivariate data, use a scatter diagram.
选择适合数据类型的图表。比较两个分布时，用背靠背茎叶图或箱线图；分类数据用条形图或饼图；双变量数据用散点图。
Frequency polygons and cumulative frequency curves are useful for showing the shape of a distribution and for finding the median and quartiles.
频数多边形和累积频数曲线有助于展示分布形状，并可用于计算中位数和四分位数。
Every chart must have a clear title, labelled axes, and a key if needed. Do not insert a chart without referring to it in the text. For example: “Figure 1 shows that the boys’ box plot is shifted to the right of the girls’ box plot.”
每张图表都必须有清晰标题、坐标轴标签，必要时加图例。不要在正文中不提及就插入图表。例如：”图 1 显示男生的箱线图整体位于女生箱线图的右侧。”
5. Descriptive Statistics: Averages and Spread | 描述统计：平均数与离散程度
Use the mean, median, and mode as measures of central tendency. The mean is calculated by summing all values and dividing by the number of values.
用平均数、中位数和众数作为集中趋势的度量。平均数的计算方法是将所有数值相加再除以数值个数。
x̄ = Σx / n
The range and interquartile range (IQR) measure spread. IQR = Q₃ − Q₁. A smaller IQR means the middle 50% of data is more consistent.
极差和四分位距（IQR）度量离散程度。IQR = Q₃ − Q₁。IQR 越小，说明中间 50% 的数据越集中。
Standard deviation is another important measure, especially when comparing two groups with similar means. A low standard deviation indicates that most values are close to the mean.
标准差是另一个重要度量，尤其在两组平均数相近时用来比较。标准差较小表明大多数数值接近平均数。
6. Bivariate Analysis and Correlation | 双变量分析与相关
If your hypothesis compares two numerical variables, draw a scatter diagram. Describe the relationship as positive, negative, or no correlation.
如果你的假设比较两个数值变量，先画散点图。将关系描述为正相关、负相关或无相关。
Correlation does not imply causation. Writing “there is a positive correlation between revision time and test score” is correct; writing “revision time causes higher scores” is too strong unless the design supports it.
相关不等于因果。写 “复习时间与考试成绩呈正相关” 是正确的；写 “复习时间导致成绩提高” 过于绝对，除非研究设计支持。
You may calculate a line of best fit, but only use it for interpolation within the data range. Extrapolation outside the data range can be unreliable.
你可以计算最佳拟合线，但只能用于数据范围内的内插预测。超出数据范围的外推可能不可靠。
For ranked data, Spearman’s rank correlation coefficient is often more suitable than drawing a line of best fit.
对于等级数据，斯皮尔曼秩相关系数通常比绘制最佳拟合线更合适。
7. Writing the Introduction and Aims | 撰写引言与目标
The introduction should explain why the topic is interesting and state the hypothesis clearly. Use the present tense for the aim and include a short prediction with a reason.
引言应解释主题为何值得研究，并清楚地陈述假设。目标用现在时表达，并附上简短的预测及理由。
Model introduction: “The aim of this investigation is to compare the handspan of Year 11 boys and girls. I predict that boys will have a larger average handspan because, on average, males tend to have larger bone structure.”
范文引言：”本次调查的目标是比较 11 年级男生和女生的手掌跨度。我预测男生的平均手掌跨度更大，因为男性骨骼结构通常更大。”
Keep the introduction concise. One paragraph is usually enough for IGCSE level, but it must clearly set up the purpose of the whole report.
引言保持简洁。IGCSE 水平通常一段就够，但必须清楚地交代整份报告的目的。
8. Writing the Method Section | 撰写方法部分
Write the method in the past tense and passive voice where possible: “A sample of 60 students was selected using a random number generator from the Year 11 register.”
方法部分用过去时，并尽量使用被动语态：”使用随机数生成器从 11 年级名册中抽取了 60 名学生。”
List the materials clearly:
清晰列出材料：
- Ruler or tape measure | 直尺或卷尺
- Recording sheet | 记录表
- Calculator | 计算器
Then describe exactly how the handspan was measured, for example from
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