📚 Cambridge IGCSE Statistics Year 10: Key Points for Practical Investigations | 剑桥IGCSE统计 Year 10：实验与实践考核要点
In Cambridge IGCSE Statistics, the practical or experimental assessment focuses on your ability to plan investigations, collect and present data, and draw valid conclusions. This article explains the essential skills you need to demonstrate in such tasks and exam questions, including designing experiments, choosing sampling methods, controlling variables, processing data, and evaluating your work. Mastering these points will help you think like a statistician and succeed in both coursework-style projects and Paper 2 application questions.
在剑桥 IGCSE 统计学中，实验或实践考核重点考察你规划调查、收集和呈现数据以及得出有效结论的能力。本文详细讲解在这类任务和考试题目中必须展示的核心技能，涵盖实验设计、抽样方法选择、控制变量、数据处理以及对工作的评估。掌握这些要点将帮助你像统计学家一样思考，并在项目式作业和 Paper 2 的应用题中取得成功。
1. Understanding the Practical Assessment Focus | 理解实践考核重点
The practical aspect of Cambridge IGCSE Statistics (0980) is integrated into written papers rather than assessed through a separate coursework component. Exam questions often ask you to describe how to carry out a statistical investigation, comment on the design of an experiment, or suggest improvements to a data collection method. Your answers need to show clear understanding of randomisation, replication, control of extraneous variables, and the avoidance of bias.
剑桥 IGCSE 统计学（0980）的实践环节融入书面试卷，而非单独通过课程作业评估。考试题目常常要求你描述如何开展一项统计调查、评价某个实验的设计，或者对数据收集方法提出改进建议。你的回答需要清晰体现对随机化、重复、控制无关变量以及避免偏差的理解。
Assessment objectives AO2 and AO3 are particularly relevant: AO2 involves processing, presenting and interpreting data; AO3 involves planning and carrying out investigations and interpreting the results. Thus, a ‘practical’ question may present a scenario and ask you to identify weaknesses in the plan, explain how to select a sample, or evaluate the reliability of conclusions.
评估目标 AO2 和 AO3 尤其相关：AO2 涉及处理、呈现和解读数据；AO3 涉及计划和开展调查并解释结果。因此，所谓“实践”题可能会给出一个情景，然后要求你指出计划中的缺陷、说明如何选取样本，或评价结论的可靠性。
2. Planning a Statistical Investigation | 规划统计调查
Every investigation starts with a clear hypothesis or research question. In the exam, you must be able to state a testable hypothesis, such as ‘Plant A grows taller than Plant B under the same conditions’ or ‘There is an association between revision time and test scores’. The hypothesis must be specific and measurable.
每项调查都始于明确的假设或研究问题。在考试中，你必须能够陈述一个可检验的假设，例如“在相同条件下植物 A 比植物 B 长得更高”或“复习时长与考试成绩之间存在关联”。假设必须具体且可度量。
Your plan should identify the variables involved: the independent variable (what you change), the dependent variable (what you measure), and the controlled variables (factors kept constant). For example, in an experiment comparing the effect of two fertilisers on plant height, the independent variable is the type of fertiliser, the dependent variable is plant height, and controlled variables could include water amount, light exposure, soil type, and pot size.
你的方案应该明确涉及的变量：自变量（你改变的量）、因变量（你测量的量）和受控变量（保持恒定的因素）。例如，在比较两种肥料对植物高度影响的实验中，自变量是肥料种类，因变量是植物高度，受控变量包括浇水量、光照时间、土壤类型和盆的大小。
Finally, decide how many measurements or trials are needed. A larger sample size increases the reliability of the results. Mentioning replication, such as using at least 10 plants for each fertiliser, demonstrates good practice.
最后，要确定需要多少次测量或试验。较大的样本量可以提高结果的可靠性。提及重复，比如每种肥料至少使用 10 株植物，能体现出良好的实验规范。
3. Choosing Sampling Methods and Avoiding Bias | 选择抽样方法并避免偏差
When you cannot study a whole population, a well-chosen sample is essential. The syllabus expects you to know and compare simple random sampling, systematic sampling, stratified sampling, quota sampling, and opportunity sampling. Understand the advantages and disadvantages of each.
当你无法研究整个总体时，选择合适的样本至关重要。大纲要求你了解并比较简单随机抽样、系统抽样、分层抽样、配额抽样和便利抽样。要清楚每种方法的优缺点。
| Method | Description & Key Features |
|---|---|
| Simple Random Sampling | Every member has an equal chance of being chosen; requires a sampling frame and random number generator. Minimises bias. |
| Systematic Sampling | Select every kth member after a random start. Quick but can be biased if there is a hidden pattern. |
| Stratified Sampling | Population divided into groups (strata); sample taken from each in proportion to its size. Reflects population structure accurately. |
| Quota Sampling | Interviewer selects fixed numbers of people with certain characteristics. Not random; can introduce selection bias. |
| Opportunity Sampling | Use who is available. Convenient but likely to be unrepresentative. |
| 方法 | 描述与关键特征 |
|---|---|
| 简单随机抽样 | 每个成员被选中的几率均等；需要抽样框和随机数生成器。偏差最小。 |
| 系统抽样 | 随机起点后每隔 k 个选取一个。快速，但如果存在隐藏模式可能产生偏差。 |
| 分层抽样 | 总体分成若干层，按比例从每层抽取样本。能准确反映总体结构。 |
| 配额抽样 | 访问员选择固定数量的具有特定特征的人。非随机，可能引入选择偏差。 |
| 便利抽样 | 使用最方便获得的对象。方便但很可能不具代表性。 |
In practical questions, always suggest using random numbers to pick items from a numbered list for simple random sampling. Highlight that bias arises when some members are more likely to be selected than others, or when the sample is too small to represent the population.
在实践题中，对于简单随机抽样，务必建议使用随机数从编号列表中选取项目。要强调当某些成员被选中的可能性高于其他成员，或者样本太小无法代表总体时，就会产生偏差。
4. Designing Questionnaires and Experiments | 设计问卷与实验
If an investigation involves a survey, you must design a questionnaire that avoids leading or ambiguous questions. Questions should be clear, unbiased, and easy to answer. For example, instead of ‘Don’t you think the new menu is great?’, ask ‘How would you rate the new menu? (Excellent, Good, Average, Poor)’. Always include mutually exclusive response options and consider whether open or closed questions are appropriate.
如果调查涉及问卷，你必须设计一份避免诱导性或模糊问题的问卷。问题应当清晰、无偏见且易于回答。例如，不要问“你不觉得新菜单很棒吗？”，而应问“你如何评价新菜单？（极好、好、一般、差）”。务必提供互斥的选项，并考虑开放式或封闭式问题何者更合适。
For an experiment, clearly state the random allocation of treatments. If comparing two teaching methods, students should be randomly assigned to groups to avoid selection bias. Use a method like drawing names from a hat or using random numbers to ensure fairness.
对于实验，要明确说明随机分配处理。如果比较两种教学方法，应当将学生随机分到不同组，以避免选择偏差。可以采用抽签或使用随机数等方法确保公平。
Pilot studies are an important part of planning. A small-scale trial run helps identify problems with the questionnaire or experimental setup before committing resources. Mentioning a pilot study shows an extra level of practical awareness.
试点研究是规划的重要环节。小规模的试运行有助于在大范围投入前发现问卷或实验设置中的问题。提到试点研究能展示更高层次的实践意识。
5. Controlling Variables in Comparative Experiments | 比较实验中的变量控制
In any comparative experiment, only the independent variable should differ between groups. All other variables (control variables) must be kept constant to ensure a fair test. When writing exam answers, list at least three controlled variables and explain how they would be kept constant.
在任何比较实验中，各组之间只应让自变量变化。其他所有变量（控制变量）必须保持恒定，以确保公平测试。在考试答题时，至少列举三个受控变量，并说明如何使它们保持不变。
For example, in an experiment testing whether a new revision app improves test scores, the controlled variables are: the amount of study time (1 hour daily for both groups), the difficulty of the pre-test and post-test, the learning environment, and the students’ prior knowledge. You could match participants by previous grades or use randomisation to spread any differences evenly.
例如，在测试一款新复习应用程序是否提高考试成绩的实验中，受控变量包括：学习时长（两组每天均为 1 小时）、前测和后测的难度、学习环境以及学生先前知识水平。你可以根据前期成绩匹配参与者，或通过随机化让差异均匀分布。
The concept of a control group is fundamental: a group that receives no treatment or a standard treatment, providing a baseline for comparison. Always specify what the control group will do. For a fertiliser experiment, one group might receive only water, serving as the control.
对照组的概念至关重要：一组不接受处理或接受标准处理，为比较提供基线。务必明确对照组将做什么。在肥料实验中，其中一组可能只浇水，作为对照组。
6. Collecting Data Efficiently and Ethically | 高效且合乎道德地收集数据
Data collection must be accurate and consistent. When measuring, use appropriate instruments (ruler, stopwatch, scale) and record readings to a consistent degree of precision. In a practical write-up, mention that measurements should be taken at regular intervals and under identical conditions.
数据收集必须准确一致。测量时使用合适的工具（尺子、秒表、秤），并以一致的精确度记录读数。在实践报告撰写中，要指出测量应定期进行，并且在相同的条件下进行。
Ethical considerations are part of many investigations, especially those involving people. You should obtain informed consent, allow participants to withdraw at any time, and keep personal data anonymous. In a survey, explain the purpose of the study and ensure confidentiality.
伦理考量是许多调查的一部分，尤其是涉及人的调查。你应当获得知情同意，允许参与者随时退出，并保持个人数据匿名。在问卷调查中，说明研究目的并确保保密性。
Use of random number tables or calculator random number functions should be described clearly: ‘I will number the 200 students from 1 to 200 and use the random number generator on my calculator to select 40 unique numbers. I will ignore any repeats and numbers outside the range.’
应当清晰描述随机数表或计算器随机数功能的使用方法：“我将给 200 名学生从 1 到 200 编号，并用计算器的随机数发生器选出 40 个不重复的号码。忽略重复以及超出范围的数字。”
7. Organising Data: Tally Charts to Frequency Tables | 整理数据：从划记表到频数表
Once raw data is collected, it must be organised. Start with a tally chart for discrete categorical data, then create a frequency table. For continuous data, group into suitable intervals (classes). The classes must not overlap and should cover the full range. For example, heights of students can be grouped as 150 ≤ h < 160, 160 ≤ h < 170, etc.
一旦收集了原始数据，就必须加以整理。对于离散分类数据，从划记表开始，然后制作频数表。对于连续数据，要分成合适的区间（组距）。组距不得重叠，并应覆盖整个范围。例如，学生身高可按 150 ≤ h < 160，160 ≤ h < 170 等分组。
When grouping, aim for 5 to 10 classes. Too few classes hide detail; too many lose the summary purpose. Record frequencies carefully and calculate a running total if a cumulative frequency table is required later for drawing an ogive or finding the median.
分组时，目标为 5 至 10 组。组数太少会掩盖细节；太多则失去汇总的意义。仔细记录频数，如果后续需要绘制累积频数图（肩形图）或求中位数，应计算累计频数。
A two-way table is useful for bivariate categorical data, such as gender against preferred mode of transport, enabling you to examine relationships and later calculate probabilities.
对于双变量分类数据，双向表格非常有用，例如性别与偏好交通方式的对照表，帮助你考察关系并后续计算概率。
8. Presenting Data: Choosing the Right Diagram | 呈现数据：选择合适的图表
Different data types require different diagrams. Use a bar chart for categorical data (with gaps between bars), a pie chart to show proportions of a whole, and a histogram for grouped continuous data. Remember that in a histogram, the area of each bar represents frequency, so frequency density = frequency ÷ class width must be calculated if class widths are unequal.
不同的数据类型需要不同的图表。分类数据使用条形图（条形之间有间隙），饼图用于展示整体中各部分的比例，直方图则适用于分组连续数据。切记在直方图中，每个条形的面积代表频数，若组距不等，需计算频率密度 = 频数 ÷ 组距。
A cumulative frequency curve (ogive) is excellent for estimating medians, quartiles, and percentiles. Plot cumulative frequency against the upper class boundary, and a smooth curve is drawn. Use it to read off values at 25%, 50%, 75% positions. Box plots (box-and-whisker plots) neatly summarise five-number summaries: minimum, Q₁, median, Q₃, maximum.
累积频数曲线（肩形图）非常适合估计中位数、四分位数和百分位数。以累积频数为纵轴、组上限为横轴描点，并绘制平滑曲线。通过它读取 25%、50%、75% 位置对应的数值。箱线图（盒须图）则精炼地概括五数综合：最小值、Q₁、中位数、Q₃、最大值。
For showing the relationship between two numerical variables, use a scatter graph. Plot the independent variable on the x‑axis and dependent on the y‑axis. Describe the correlation (positive, negative, or none) and, if appropriate, add a line of best fit to make predictions. Always comment on outliers.
对于展示两个数值变量之间的关系，使用散点图。自变量标注在 x 轴，因变量标注在 y 轴。描述相关性（正、负或无），如果合适，添加最佳拟合线以进行预测。务必对异常值加以评论。
9. Calculating Summary Statistics | 计算汇总统计量
Measures of central tendency (mean, median, mode) and measures of dispersion (range, interquartile range, standard deviation) are vital in practical conclusions. Use the mean and standard deviation for symmetric data with no extreme outliers; use the median and IQR for skewed data or when outliers are present.
集中趋势的度量（平均数、中位数、众数）和离散程度的度量（全距、四分位距、标准差）在实践结论中至关重要。对于对称且无极端异常值的数据，使用平均数和标准差；对于偏态数据或存在异常值的情况，使用中位数和四分位距。
The mean is calculated as x̄ = Σx / n. The standard deviation for a sample can be found using the formula:
s = √[ Σ(x – x̄)² / (n – 1) ]
平均数公式为 x̄ = Σx / n。样本标准差可使用以下公式计算：
s = √[ Σ(x – x̄)² / (n – 1) ]
In exams, you may also work with raw data or frequency tables to compute an estimate of the mean, such as Σfx / Σf. For grouped data, use the class midpoint (mid‑interval value) as x. Clearly show each step to avoid arithmetic errors.
考试中你可能还要处理原始数据或频数表，以计算平均数的估计值，如 Σfx / Σf。对于分组数据，使用组中值作为 x。清晰展示每一步骤，避免计算错误。
10. Interpreting Results and Drawing Conclusions | 解读结果并得出结论
A practical investigation is not complete without a conclusion that relates back to the original hypothesis. State whether the data supports the hypothesis, and quote figures such as the difference between means, the correlation coefficient, or the median values. Avoid overstating certainty; use language like ‘the evidence suggests’ rather than ‘proves’.
一项实践调查如果没有将结论与最初假设联系起来，就是不完整的。陈述数据是否支持假设，并引用数字，如平均数之间的差异、相关系数或中位数值。避免夸大确定性，使用诸如“证据表明”而非“证明”之类的措辞。
When comparing two groups, calculate and compare summary statistics, but also consider the overlap between distributions. For instance, two box plots drawn on the same scale can visually show the difference in medians and the IQRs. If the boxes overlap substantially, the difference might not be significant in context.
当比较两个组时，计算并比较汇总统计量，但也要考虑分布之间的重叠。例如，用相同尺度绘制两个箱线图可以直观展示中位数和四分位距的差异。如果箱体大量重叠，这种差异在具体背景下可能并不显著。
Always relate the conclusion to the real-world context of the investigation. If you were testing a new teaching method and found only a small improvement, discuss whether it is educationally meaningful.
务必将结论与调查的现实背景联系起来。如果你在测试一种新的教学方法并只发现微小的改善，要讨论这种改善在教育上是否有意义。
11. Evaluating the Investigation: Limitations and Improvements | 评估调查：局限与改进
A high-scoring practical answer always includes an evaluation. Identify at least two limitations—these could be about sample size, sampling method, measurement errors, uncontrolled variables, or the time frame. For each limitation, suggest a realistic improvement.
得分高的实践答案总包含评估部分。至少指出两个局限——可能涉及样本量、抽样方法、测量误差、未受控的变量或时间框架。针对每项局限，提出一个现实的改进建议。
Common limitations include: ‘the sample size of 20 may be too small to generalise’, ‘data was only collected on one day so weather could have affected results’, ‘the questionnaire contained a leading question’, or ‘participants were self-selected so the sample was biased’. Improvements: increase sample size, collect data over several weeks, reword the question, use random selection.
常见的局限包括：“样本量只有 20 可能太小而无法推广”、“数据只在一天收集，天气可能影响结果”、“问卷中有诱导性问题”或“参与者是自我选择的，样本有偏差”。改进措施：增加样本量、在数周内收集数据、修改问题措辞、采用随机选择。
Always comment on the reliability and validity of your investigation. Reliability relates to repeatability; if another person followed your plan, would they get similar results? Validity concerns whether you are measuring what you intended to measure and whether the conclusions are justified. Address both.
务必评论调查的可靠性和有效性。可靠性关乎可重复性——若他人按照你的方案进行，是否会得到类似结果？有效性则关注你是否在测量你想测量的对象，以及结论是否合理。二者都应涉及。
12. Exam Tips for Practical Statistics Questions | 统计实践题考试技巧
Read the question carefully and identify the command words: ‘describe’, ‘explain’, ‘compare’, ‘evaluate’. If asked to ‘design’ an investigation, structure your answer with clear sections: hypothesis, variables, sampling, procedure, data collection, analysis plan, and evaluation.
仔细阅读题目，识别指令词：“describe”（描述）、“explain”（解释）、“compare”（比较）、“evaluate”（评估）。如果要求“设计”一项调查，答案要结构清晰，包含：假设、变量、抽样方法、步骤、数据收集、分析计划和评估。
Use technical vocabulary accurately: random sampling, stratified, control group, pilot study, unbiased, reliability, validity. Show that you understand these terms in context rather than just listing them. If a question provides a flawed plan, point out specific weaknesses and suggest specific fixes.
准确使用专业词汇：random sampling、stratified、control group、pilot study、unbiased、reliability、validity。要展示你在具体情境中理解这些术语，而不是仅仅罗列。如果题目提供了一个有缺陷的方案，要指出具体弱点并提出具体的修改建议。
Time management is crucial. In extended response questions, spend a minute planning the structure. Underline key quantitative information given, and always check why a given calculation method or diagram is appropriate. When an answer asks for ‘two reasons’, provide exactly two distinct, well-explained reasons—never just one.
时间管理至关重要。在长篇回答题中，花一分钟规划结构。对给出的关键数量信息划线，并始终检查为什么某个计算方法或图表是合适的。当要求给出“两个原因”时，务必提供两个不同且解释清晰的原因——切忌只写一个。
Finally, numerical answers must be supported by working. Even if you use a calculator, write down the formula, the substituted values, and the final rounded answer to an appropriate degree of accuracy (usually 3 significant figures). Clear working earns method marks even if the final number is wrong.
最后，数值答案必须有演算步骤支撑。即使使用计算器，也要写下公式、代入数值，并将最终答案四舍五入到适当的精确度（通常为 3 位有效数字）。过程清晰即便最后数字有误，也能获得方法
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