📚 Year 10 CAIE Statistics: Complete Syllabus Breakdown | Year 10 CAIE 统计：课程大纲全面解析
IGCSE Statistics (0470) equips Year 10 learners with essential tools to collect, analyse, and interpret data, forming a solid foundation for further study in mathematics, science, and social sciences. This article breaks down the entire CAIE syllabus into ten manageable sections, highlighting key concepts, formulas, and exam tips that are crucial for success.
IGCSE 统计（0470）为 Year 10 学生提供了收集、分析和解释数据的重要工具，为数学、科学和社会科学领域的深入学习奠定坚实基础。本文将整个 CAIE 课程大纲分解为十个模块，突出关键概念、公式和考试技巧，对取得好成绩至关重要。
1. Data Types and Collection | 数据类型与收集
Understanding data types is fundamental. Data can be qualitative (categorical) or quantitative (numerical). Quantitative data splits into discrete (counts, e.g. number of students) and continuous (measurements, e.g. height).
理解数据类型是基础。数据可以是定性（分类）或定量（数值）。定量数据分为离散（计数，如学生人数）和连续（测量，如身高）。
Primary data is collected firsthand via experiments or surveys, while secondary data comes from existing sources like government reports. Knowing the source helps assess reliability.
一手数据通过实验或调查直接收集，二手数据来自政府报告等现有来源。了解数据来源有助于评估可靠性。
Students must also distinguish between a population (the entire group) and a sample (a subset). In Year 10, you learn to design simple data-collection sheets and questionnaires, ensuring questions are clear, unbiased and able to produce the intended data type.
学生还需区分总体（整个群体）和样本（子集）。在 Year 10，你要学习设计简单的数据收集表和问卷，保证问题清晰、无偏且能产生预期的数据类型。
Be prepared to identify potential sources of bias in data collection and suggest improvements, as this appears regularly in examination scenarios.
要能够识别数据收集中潜在的偏差来源并提出改进建议，这在考试情景中经常出现。
2. Sampling Methods | 抽样方法
Sampling is used to draw conclusions about a population without surveying everyone. Common methods include random, stratified, systematic, and quota sampling. Each has distinct advantages and limitations.
抽样用于无需调查每个人即可得出关于总体的结论。常见方法包括随机抽样、分层抽样、系统抽样和配额抽样。每种方法都有独特的优点和局限性。
Random sampling gives every member an equal chance of selection, minimising bias, but it requires a complete population list. In stratified sampling, the population is divided into groups (strata) and a random sample is taken from each in proportion to its size, guaranteeing representation.
随机抽样让每个成员都有相等被选机会，减少偏差，但需要完整的总体名单。分层抽样则将总体分为层，并按各层大小比例随机抽取样本，保证代表性。
Systematic sampling selects every k-th item after a random start; it is simple but can lead to periodicity bias. Quota sampling fills predetermined numbers for each category quickly and cheaply, but it is non‑random and can introduce interviewer bias.
系统抽样在随机起点后选取每一个第 k 项，操作简单但可能导致周期性偏差。配额抽样快速、低成本地为每个类别填满预定数量，但非随机，可能引入访问员偏差。
Exam questions often ask you to identify the sampling method used in a scenario, justify your choice, and comment on advantages or disadvantages.
考试中常要求识别情景中使用的抽样方法、说明理由并评价其优缺点。
3. Representing Data: Graphs and Charts | 数据表示：图形与图表
Effective data presentation is key. Bar charts compare frequencies across categories, while pie charts show proportions of a whole. When constructing a pie chart, calculate the angle for each sector using angle = (category frequency ÷ total) × 360°.
有效的数据呈现至关重要。条形图比较不同类别的频数，饼图显示各部分占整体的比例。绘制饼图时，使用 角度 = (类别频数 ÷ 总数) × 360° 计算每个扇形的圆心角。
Stem-and-leaf diagrams order data and retain original values, making it easy to find medians and quartiles. A back‑to‑back stem‑and‑leaf diagram can compare two data sets on opposite sides of the same stem.
茎叶图将数据排序并保留原始值，便于找出中位数和四分位数。背靠背茎叶图可在同一茎的两侧比较两组数据。
Dot plots and pictograms are also examined, but you must use a key for pictograms to indicate the number each symbol represents. Multiple bar charts and component bar charts help display sub‑categories or totals.
点图和象形图也可能考查，但象形图必须使用图例说明每个符号代表的数值。复式条形图和分段条形图有助于展示子类别或总量。
For paired data, scatter diagrams reveal relationships between two variables, which leads to correlation analysis later.
对于成对数据，散点图揭示两个变量间的关系，为后续的相关性分析做铺垫。
4. Histograms and Cumulative Frequency | 直方图和累积频率
Histograms are used for continuous data. Unlike bar charts, the area of each bar represents frequency, so you must use frequency density = frequency ÷ class width. Bars are drawn with no gaps, and unequal class widths are common.
直方图用于连续数据。与条形图不同，每个直条的面积代表频数，因此必须使用频率密度 = 频数 ÷ 组距。直条之间无间隙，且组距不相等的情况很常见。
When calculating frequency density, always check class boundaries. For example, a class interval of 10 ≤ t < 20 has width 10. Plot frequency density on the vertical axis and the variable on the horizontal axis.
计算频率密度时一定要检查组界。例如，组区间 10 ≤ t < 20 的组距为 10。纵轴表示频率密度，横轴表示变量。
Cumulative frequency curves (ogives) show the running total of frequencies. Plot the points at the upper class boundary against the cumulative frequency, then join them with a smooth curve. Use the graph to estimate medians, quartiles, and percentiles.
累积频率曲线（卵形线）显示频数的累计总数。以各组上限为横坐标、累积频数为纵坐标描点，然后用光滑曲线连接。利用曲线可估算中位数、四分位数和百分位数。
The interquartile range (IQR) = upper quartile − lower quartile. It is a measure of spread less affected by extremes. You may also be asked to interpret cumulative frequency graphs to find the number of items above or below a threshold.
四分位距 (IQR) = 上四分位数 − 下四分位数。它是一种不易受极端值影响的离散度量。考试还可能要求你解释累积频率图，找出高于或低于某临界值的项目个数。
5. Measures of Central Tendency | 集中趋势测量
The three main averages are mean, median, and mode. The mean (x̄) is the sum of all values divided by the number of values: x̄ = Σx / n. For grouped data, use the midpoint of each class to approximate the mean.
三种主要平均数是均值、中位数和众数。均值（x̄）是所有值之和除以值的个数：x̄ = Σx / n。对于分组数据，使用每组的中值来近似计算均值。
The median is the middle value when data is ordered; for n values, its position is (n+1)/2. If n is even, take the mean of the two middle values. The mode is the most frequent value, useful for qualitative data.
中位数是排序后中间的值；对于 n 个值，位置 = (n+1)/2。若 n 为偶数，则取中间两值的均值。众数是出现最频繁的值，对定性数据尤其有用。
The table below summarises the key averages and their properties:
下表总结了主要平均数及其特性：
| Measure | Symbol/Formula
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