📚 Core Knowledge Review for Year 10 CCEA Statistics | Year 10 CCEA 统计：核心知识点梳理
This article provides a structured revision of the essential topics in the Year 10 CCEA Statistics course. Each section breaks down a key concept with clear explanations and worked examples, helping you build confidence as you prepare for assessments. Read through both the English and Chinese explanations to reinforce your understanding.
本文对 Year 10 CCEA 统计课程的核心知识点进行了系统梳理。每个小节都围绕一个关键概念展开，配有清晰解释和实例，帮助你在备考过程中建立信心。通过中英双语对照阅读，能够加深你对每个概念的理解。
1. Types of Data | 数据类型
Data can be classified as qualitative or quantitative. Qualitative data describes qualities or categories, such as eye colour or make of car. Quantitative data is numerical and can be further divided into discrete data, which can only take certain values (e.g. number of students), and continuous data, which can take any value within a range (e.g. height).
数据可以分为定性数据和定量数据。定性数据描述的是属性或类别，例如眼睛颜色或汽车品牌。定量数据是数值型的，可以进一步分为只能取特定值的离散数据（如学生人数）和在一定范围内可以取任意值的连续数据（如身高）。
Recognising the data type is crucial because it determines which diagrams and calculations are appropriate. For instance, we use bar charts for qualitative data and histograms for continuous data.
识别数据类型非常重要，因为它决定了适合使用哪种图表和计算方法。例如，定性数据使用条形图，而连续数据使用直方图。
2. Collecting Data: Sampling Methods | 数据收集：抽样方法
A population is the entire group we want information about. A sample is a smaller group selected from the population. Random sampling gives every member an equal chance of being chosen, reducing bias. Stratified sampling divides the population into groups (strata) and takes a random sample from each stratum in proportion to its size.
总体是我们想要了解的全部对象。样本是从总体中选出的一个较小群体。随机抽样使每个成员都有同等被选中的机会，能减少偏差。分层抽样先将总体分成若干层（层），然后从每一层中按比例随机抽取样本。
Other methods include systematic sampling (selecting every nth item) and cluster sampling. Understanding the strengths and limitations of each method helps in evaluating the reliability of statistical conclusions.
其他方法包括系统抽样（每隔一定数量选取一个样本）和整群抽样。理解每种方法的优缺点有助于评估统计结论的可靠性。
3. Frequency Tables and Diagrams | 频数表与统计图
A frequency table organises raw data into groups or individual values, showing how often each occurs. From a frequency table we can calculate totals and construct bar charts, pie charts, or pictograms. The vertical axis of a bar chart should always start at zero to avoid misleading representation.
频数表将原始数据按组别或数值进行整理，显示每个取值出现的次数。利用频数表我们可以计算总和，并绘制条形图、饼图或象形图。条形图的纵轴应该始终从零开始，以避免误导性的呈现。
For discrete data, bar charts have gaps between bars; for continuous data, we use histograms with no gaps. A stem-and-leaf diagram keeps the original data values while showing the shape of the distribution.
对于离散数据，条形图的柱子之间有间隙；对于连续数据，我们使用无间隙的直方图。茎叶图不仅能保留原始数据值，还能展示分布形态。
4. Measures of Central Tendency | 集中趋势的度量
The three main averages are the mean, median, and mode. The mean is calculated by summing all values and dividing by the number of values. The median is the middle value when data is ordered. The mode is the most frequent value.
三种主要的平均数是平均数、中位数和众数。平均数通过所有数值之和除以数值个数求得。中位数是将数据排序后位于中间的值。众数是出现频率最高的值。
Choosing the appropriate average depends on the data type and presence of outliers. The mean is sensitive to extreme values, while the median is robust. The mode is particularly useful for categorical data.
选择适当的平均数取决于数据类型和是否存在异常值。平均数对极端值敏感，而中位数较为稳健。众数特别适用于类别数据。
5. Measures of Spread: Range and Interquartile Range | 离散程度的度量：极差与四分位距
The range is the difference between the largest and smallest values. It gives a basic idea of spread but can be affected by outliers. The interquartile range (IQR) is the difference between the upper quartile (Q₃) and the lower quartile (Q₁), representing the spread of the middle 50% of data.
极差是最大值与最小值之差，能基本反映数据的分散程度，但容易受异常值影响。四分位距（IQR）是上四分位数（Q₃）与下四分位数（Q₁）之差，代表中间 50% 数据的分布范围。
To find quartiles, first order the data. The median is Q₂. The lower quartile is the median of the lower half, and the upper quartile is the median of the upper half. If the number of data points is odd, the median itself is not included in the halves.
要找到四分位数，首先将数据排序。中位数即 Q₂。下四分位数是下半部分数据的中位数，上四分位数是上半部分数据的中位数。如果数据个数为奇数，中位数本身不包含在上下半部中。
6. Box Plots | 箱线图
A box plot (or box-and-whisker diagram) visually represents the five-number summary: minimum, lower quartile, median, upper quartile, and maximum. The box spans from Q₁ to Q₃, with a line inside marking the median. Whiskers extend to the minimum and maximum values, unless there are outliers.
箱线图（又称盒须图）用图形表示五数概括：最小值、下四分位数、中位数、上四分位数和最大值。箱子从 Q₁ 延伸到 Q₃，内部一条线标出中位数。须线延伸到最小值和最大值，除非存在异常值。
Box plots are excellent for comparing distributions across different data sets side by side. They clearly show the centre, spread, and any skewness in the data.
箱线图非常适合并排比较不同数据集的分布情况，能清晰显示数据的中心、离散程度和任何偏态。
7. Cumulative Frequency and Cumulative Frequency Graphs | 累积频数与累积频数图
Cumulative frequency is the running total of frequencies as you move through the classes. A cumulative frequency table adds a column where each entry is the sum of the frequency for that class and all previous classes.
累积频数是随着组别推进的频数累计总和。累积频数表会添加一列，其中每个条目是该组及之前所有组的频数之和。
Plotting cumulative frequency against the upper class boundary gives an S-shaped curve. You can use this graph to estimate the median (at 50% of total frequency), quartiles (at 25% and 75%), and other percentiles. The interquartile range can be read directly from the graph.
将累积频数对应组上限绘图，会得到一条 S 形曲线。利用该图可以估算中位数（总频数的 50% 处）、四分位数（25% 和 75% 处）以及其他百分位数。四分位距可直接从图中读出。
8. Basic Probability | 基本概率
Probability measures how likely an event is to happen, expressed as a fraction, decimal, or percentage between 0 and 1. A probability of 0 means impossible; 1 means certain. The sum of probabilities of all mutually exclusive outcomes equals 1.
概率衡量事件发生的可能性，用 0 到 1 之间的分数、小数或百分数表示。概率为 0 表示不可能，为 1 表示必然。所有互斥结果的概率之和等于 1。
Experimental probability is based on trials or experiments, while theoretical probability is based on equally likely outcomes. The expected frequency of an event is the probability multiplied by the number of trials.
实验概率基于试验或实验结果，而理论概率基于等可能的结果。事件的期望频数是概率乘以试验次数。
9. Probability Tree Diagrams | 概率树形图
Tree diagrams help handle combined events, especially when there are multiple stages. Branches represent possible outcomes, with probabilities written on them. The probabilities on branches from a single point must add up to 1.
树形图有助于处理组合事件，尤其是有多个阶段的情况。树枝代表可能的结果，上面标有概率。从同一点分出的各树枝概率之和必须为 1。
To find the probability of a sequence of events, multiply along the branches. If there are two or more paths leading to the same outcome, add the probabilities for those paths. Remember to consider whether events are independent or conditional; in Year 10, most tree diagrams assume replacement or independence unless stated otherwise.
要求一系列事件的概率，沿树枝相乘。如果有两条或多条路径导向同一结果，则将这些路径的概率相加。注意事件是独立还是条件性的；Year 10 阶段若无特别说明，多数树形图假定有放回或独立。
10. Scatter Graphs and Correlation | 散点图与相关性
A scatter graph shows the relationship between two variables. The explanatory (independent) variable goes on the x-axis, and the response (dependent) variable on the y-axis. The pattern of points can reveal correlation: positive (as one increases, the other tends to increase), negative, or no correlation.
散点图显示两个变量之间的关系。解释变量（自变量）放在 x 轴，响应变量（因变量）放在 y 轴。点的分布模式可以揭示相关性：正相关（一个增大，另一个也趋于增大）、负相关或无相关。
Correlation does not imply causation. You can describe correlation as strong, moderate, or weak. A line of best fit can be drawn by eye to model the trend and make predictions, but predictions outside the range of data (extrapolation) are unreliable.
相关性并不意味着因果关系。你可以将相关性描述为强、中等或弱。可以凭目测画出一条最佳拟合线来模拟趋势并进行预测，但在数据范围之外的预测（外推）是不可靠的。
11. Interpreting Statistical Diagrams and Misleading Graphs | 解读统计图与误导性图表
Always examine scales, labels, and the starting point of axes carefully. A truncated vertical scale can exaggerate small differences. Missing labels and inconsistent class intervals can distort interpretation.
务必仔细检查坐标轴的刻度、标签和起点。截断的纵轴会夸大微小差异。缺少标签或组距不一致都可能曲解信息。
Be able to compare two data sets using back-to-back stem-and-leaf diagrams or dual bar charts. When comparing distributions, comment on an average (median/mean) and a measure of spread (range/IQR), linking back to the context of the question.
要能够使用背靠背茎叶图或双条形图比较两组数据。在比较分布时，需要对平均数（中位数/平均数）和离散度量（极差/四分位距）进行评述，并结合问题背景加以说明。
Published by TutorHao | CCEA Statistics Revision Series | aleveler.com
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