📚 Year 8 CCEA Statistics: Formula & Theorem Quick Reference Guide | CCEA 八年级统计：公式定理速查手册
Welcome to your Year 8 CCEA Statistics quick reference guide. This handbook summarises the essential formulas, definitions and theorems you need to know for interpreting data, calculating summary statistics, and understanding probability. Keep this page handy for revision and homework.
欢迎使用八年级 CCEA 统计速查手册。本手册归纳了你在理解数据、计算汇总统计量和掌握概率时必须掌握的核心公式、定义和定理。请保存此页用作复习和作业参考。
1. Mean (Arithmetic Average) | 算术平均数
The mean is the sum of all values divided by the number of values. It is the most common measure of central tendency.
平均数等于所有数值之和除以数值的个数，是最常用的集中趋势度量。
Formula:
公式：
Mean = (∑x) / n or x̄ = Σx / n
Where ∑x represents the sum of all data values, and n is the total number of values.
其中 ∑x 表示所有数据值的和，n 表示数据值的总个数。
The mean is sensitive to outliers, which can pull the average up or down. For a more robust measure, use the median.
平均数对异常值敏感，异常值会拉高或拉低平均值。如需更稳健的度量，请使用中位数。
2. Median | 中位数
The median is the middle value in an ordered data set. It splits the data into two equal halves.
中位数是排序后数据集的中间值，将数据分为相等的两半。
To find the median:
求中位数的步骤：
1. Arrange the data in ascending order. 2. If the number of observations n is odd, the median is the (n+1)/2 th value. 3. If n is even, the median is the average of the n/2 th and (n/2 + 1) th values.
1. 将数据按升序排列。2. 若数据个数 n 为奇数，中位数即为第 (n+1)/2 个数。3. 若 n 为偶数，中位数为第 n/2 和第 (n/2 + 1) 个数的平均值。
Median position = (n + 1) ÷ 2 (for odd n)
Use this position to locate the median in the ordered list.
利用该位置在排序列表中定位中位数。
The median is not affected by outliers, making it a better measure of centre for skewed distributions.
中位数不受异常值影响，因此对于偏态分布是更好的中心度量。
3. Mode | 众数
The mode is the data value that occurs with the highest frequency. A data set can have one mode (unimodal), two modes (bimodal), or more than two modes (multimodal). If no value repeats, there is no mode.
众数是出现频率最高的数据值。数据集可能有一个众数（单峰）、两个众数（双峰）或多于两个众数（多峰）。若没有重复值，则无众数。
The mode is the only measure of centre that can be used with categorical (non-numerical) data.
众数是唯一可用于分类（非数字）数据的集中趋势度量。
4. Range | 极差
The range is a measure of spread. It shows how far apart the smallest and largest values are.
极差是一种离散程度的度量，表示最小值与最大值之间的间隔。
Formula:
公式：
Range = Maximum value – Minimum value
Although easy to calculate, the range only uses two data points and can be heavily influenced by outliers.
虽然计算简单，但极差仅使用两个数据点，且极易受异常值影响。
5. Probability Basics | 概率基础
Probability measures how likely an event is to happen. It is expressed as a number between 0 and 1, a fraction, a decimal, or a percentage.
概率衡量事件发生的可能性，用 0 到 1 之间的数、分数、小数或百分数表示。
The theoretical probability formula:
理论概率公式：
P(Event) = Number of favourable outcomes / Total number of possible outcomes
A probability of 0 means the event is impossible; a probability of 1 means it is certain.
概率为 0 表示事件不可能发生；概率为 1 表示事件必然发生。
The complement rule: P(not A) = 1 – P(A).
互补事件规则：P(非 A) = 1 – P(A)。
6. Experimental and Theoretical Probability | 实验概率与理论概率
Theoretical probability is determined by reasoning about equally likely outcomes. Experimental probability is based on actual trials or experiments.
理论概率通过对等可能结果进行推理得出。实验概率基于实际试验或实验。
Experimental probability formula:
实验概率公式：
Experimental probability = Number of times the event occurs / Total number of trials
As the number of trials increases, the experimental probability tends to get closer to the theoretical probability (the Law of Large Numbers).
随着试验次数增加，实验概率会趋近于理论概率（大数定律）。
7. Mean from a Frequency Table | 频数表求平均数
When data are grouped into a frequency table, the mean is calculated by multiplying each data value by its frequency, summing these products, and then dividing by the total frequency.
当数据整理在频数表中时，计算平均数的方法是：将每个数据值乘以其频数，求和后再除以总频数。
Formula:
公式：
Mean = Σ(f × x) / Σf
Where f is the frequency of each value x. This formula works for discrete data; for grouped continuous data, use the midpoint of each class interval as x.
其中 f 是每个数值 x 对应的频数。该公式适用于离散数据；对于分组连续数据，使用区间的中点作为 x。
8. Types of Data | 数据类型
Data are classified as qualitative (categorical) or quantitative (
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