📚 Year 11 Edexcel Statistics: Vocabulary & Terminology Quick-Memorisation Guide | Year 11 Edexcel 统计：词汇术语速记指南
Mastering key statistical terminology is your first step to success in Edexcel GCSE Statistics. This quick-memorisation guide presents essential terms in a bilingual format, helping you to retain definitions and apply them confidently in exams.
掌握核心统计术语是你攻克 Edexcel GCSE 统计的第一步。这份速记指南以双语呈现关键概念，帮助你在考试中牢固记忆、灵活运用。
1. Population, Sample & Census | 总体、样本与普查
A population is the entire collection of individuals, objects, or measurements you wish to study. A sample is a subset of the population selected to draw conclusions about the whole. A census collects data from every member of the population.
总体是研究中所有个体的集合。样本是从总体中选出的一个子集，用于推断总体特征。普查则是对总体中每一个体都进行数据采集。
The sampling frame is the list of all members of the population from which a sample can be selected. If the sampling frame is inaccurate or incomplete, selection bias occurs.
抽样框是总体所有成员的名单，供抽取样本使用。若抽样框不准确或不完整，就会产生选择偏差。
Memory trick: ‘Population = Perfectly Everyone; Sample = Small piece that tastes like the whole; Census = Counting Every Single One.’
记忆口诀：总体 = 全部；样本 = 尝一口知整锅味；普查 = 人人点到。
2. Data Types: Qualitative, Quantitative, Discrete & Continuous | 数据类型：定性、定量、离散与连续
Qualitative (categorical) data are non-numerical descriptions, such as eye colour or type of pet. Quantitative data are numerical and can be further classified as discrete or continuous.
定性（分类）数据是非数值的描述，如眼睛颜色、宠物类型。定量数据是数值型的，可进一步分为离散和连续。
Discrete data can only take specific, separated values, often counts: number of siblings (0, 1, 2, …). Continuous data can take any value within a range, usually measurements: height, weight, time.
离散数据只能取特定的、分隔的值，通常是计数，如兄弟姐妹数（0, 1, 2…）。连续数据在某个区间内可取任意值，通常是测量结果，如身高、体重、时间。
Recall: ‘Discrete like steps on stairs – you cannot stop between steps; Continuous like water flowing from a tap – it can be any amount.’
联想：离散如楼梯台阶，无法停在两级之间；连续如流水，可以任意取值。
3. Data Collection: Primary & Secondary Data | 数据收集：一手与二手数据
Primary data are collected first-hand by the researcher for a specific purpose (e.g. a well-designed questionnaire). Secondary data are obtained from existing sources (e.g. government statistics, internet databases).
一手数据由研究者为特定目的直接收集（如精心设计的问卷）。二手数据来自已有资料（如政府统计、网络数据库）。
Primary data are usually more accurate and up-to-date but expensive and time-consuming to collect. Secondary data are cheaper and quicker to obtain but may be outdated or not exactly fit the research question.
一手数据通常更准确、更新，但耗时费钱；二手数据更便宜快捷，但可能过时或不完全匹配研究问题。
Think: ‘Primary = Proactively produced; Secondary = Second-hand.’
助记：一手 = 亲自生产；二手 = 现成借用。
4. Sampling Methods: Random, Stratified, Systematic & Biases | 抽样方法：随机、分层、系统与偏差
In simple random sampling, every member of the population has an equal chance of being selected, often using random number generators. This reduces bias but can be expensive to implement.
在简单随机抽样中，总体每个成员被选中的机会均等，常用随机数生成器。这能减少偏差，但实施成本较高。
Stratified sampling divides the population into distinct groups (strata) and takes a random sample from each in proportion to its size. This guarantees representation of all subgroups.
分层抽样将总体划分为不同的层，按比例从每层抽取随机样本，保证所有子群的代表性。
Systematic sampling selects every k-th item after a random start. Quota sampling selects a fixed number of participants from each category, but non-randomly. Convenience sampling uses subjects that are easiest to reach, which often leads to strong selection bias.
系统抽样是随机起点后每隔k个抽取一个。配额抽样从每个类别选取固定数量，但非随机。便利抽样则选取最容易接触的对象，往往导致严重的选择偏差。
Avoiding bias is crucial: selection bias when the sample is not representative; non-response bias when certain members refuse to participate. Always check the sampling frame and method.
避免偏差至关重要：选择偏差源于样本不具代表性；无回应偏差因部分成员拒绝参与。务必核查抽样框与方法。
5. Measures of Central Tendency: Mean, Median & Mode | 集中量数：平均数、中位数与众数
The arithmetic mean (x̄) is the sum of all values divided by the number of values. It is affected by extreme values and is most suitable for symmetric data.
算术平均数（x̄）是所有数值之和除以数值个数。它受极端值影响，最适合对称数据。
x̄ = Σx / n
The median is the middle value in an ordered list. For n values, the median position is (n + 1) / 2. It is resistant to outliers and is preferred for skewed distributions.
中位数是排序后位于中间的值。中位数的位置为 (n + 1)/2。它不受异常值干扰，适用于偏态分布。
The mode is the most frequently occurring value or category. A dataset can have one mode (unimodal), two modes (bimodal) or more. Mode is the only measure of central tendency for qualitative data.
众数是出现频率最高的值或类别。数据集可以有单众数、双众数或多众数。众数是定性数据唯一可用的集中量数。
Memory: ‘Mean – you actually calculate; Median – middle; Mode – Most Often.’
记忆：平均数 = 计算均值；中位数 = 中间位置；众数 = 出现最多。
6. Measures of Spread: Range, IQR & Standard Deviation | 离散量数：极差、四分位距与标准差
Range = maximum value − minimum value. It is the simplest measure of spread but is highly affected by outliers.
极差 = 最大值 − 最小值。它是最简单的离散量数，但极易受异常值影响。
The interquartile range (IQR) = Q₃ − Q₁, representing the spread of the middle 50% of ordered data. IQR is robust against outliers.
四分位距（IQR）= Q₃ − Q₁，代表排序后中间50%数据的离散程度。IQR对异常值稳健。
Standard deviation measures the average distance of data points from the mean. For a sample, we use:
标准差衡量数据点偏离平均值的平均距离。样本标准差公式为：
s = √[ Σ(x − x̄)² / (n − 1) ]
A small standard deviation means data are clustered tightly around the mean; a large one means more spread.
标准差小表示数据紧密聚集在均值附近；标准差大表示数据更分散。
7. Outliers and Their Identification | 异常值及其识别
An outlier is a data point that lies an abnormal distance from other values. Outliers may be due to measurement error, natural variation, or indicate something significant about the process.
异常值是与其余数据显著不同的极端值。异常值可能源于测量误差、自然变异或反映过程的某种重要特征。
The standard IQR rule for outliers: Lower fence = Q₁ − 1.5 × IQR, Upper fence = Q₃ + 1.5 × IQR. Any value outside these fences is considered an outlier.
识别异常值的标准IQR法则：下界 = Q₁ − 1.5 × IQR，上界 = Q₃ + 1.5 × IQR。落在界外的值即被视为异常值。
Sometimes 2 standard deviations from the mean is also used in symmetric distributions: any value outside (x̄ − 2s, x̄ + 2s) may be treated as an outlier.
有时也在对称分布中使用均值±2个标准差：超出 (x̄ − 2s, x̄ + 2s) 区间的值可视为异常值。
8. Probability Essentials: Sample Space, Events & Diagrams | 概率基础：样本空间、事件与图示
The sample space is the set of all possible outcomes of a random experiment. An event is any subset of the sample space. Probability of an event = (number of favourable outcomes) / (total number of possible outcomes).
样本空间是随机试验所有可能结果的集合。事件是样本空间的任意子集。事件概率 = (有利结果数) / (可能结果总数)。
Venn diagrams show unions (A ∪ B), intersections (A ∩ B) and complements (A’). Tree diagrams help model sequential events: multiply along branches for combined probabilities, add for mutually exclusive branches.
文氏图显示并集 (A ∪ B)、交集 (A ∩ B) 及补集 (A’)。树状图用于模拟序列事件：沿分支相乘得联合概率，互斥分支则相加。
Probability always lies between 0 and 1 inclusive. 0 means impossible; 1 means certain.
概率永远介于0和1之间。0表示不可能事件；1表示必然事件。
9. Probability Rules: Mutually Exclusive, Independent & Conditional | 概率法则：互斥、独立与条件
Two events are mutually exclusive if they cannot occur at the same time. Then P(A ∩ B) = 0 and P(A ∪ B) = P(A) + P(B).
若两事件不能同时发生，则互斥，有 P(A ∩ B) = 0 且 P(A ∪ B) = P(A) + P(B)。
Independent events have no influence on each other: P(A ∩ B) = P(A) × P(B). Independence is not the same as mutual exclusivity.
独立事件互不影响：P(A ∩ B) = P(A) ×
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