📚 AS Edexcel Statistics: Key Vocabulary Quick-Reference Guide | AS Edexcel 统计：核心术语速记指南
Mastering statistical vocabulary is not just about passing an exam — it is the key to thinking clearly with data. This guide breaks down the essential terms you will meet in AS Edexcel Statistics, pairing each English definition with a Chinese explanation to build true bilingual understanding. Whether you are preparing for a written paper or tackling a data-analysis problem, a solid command of these terms will give you confidence and precision.
掌握统计术语不仅是应付考试，更是用数据清晰思考的关键。本指南拆解你在 AS Edexcel 统计课程中会遇到的核心词汇，将每个英文定义与中文解释配对，帮助你建立扎实的双语理解。无论你是在准备笔试还是处理数据分析题，牢牢掌握这些术语都能让你信心十足、表达精准。
1. Population, Sample & Sampling Frame | 总体、样本与抽样框
A population is the entire set of individuals or items that we want information about. A sample is a subset of the population, selected to represent it. A sampling frame is a list of all the members of the population from which the sample is drawn. For example, if you are studying the heights of students in a school, the population is all students in that school, and a sampling frame could be the school register.
总体指的是我们希望获取信息的全部个体或项目。样本是从总体中选出的一个子集，用以代表总体。抽样框是列出总体中所有成员的一份清单，样本即从中抽取。例如，如果你在研究一所学校学生的身高，总体就是该校所有学生，而抽样框可以是学校的花名册。
2. Census vs Sample Survey | 普查与抽样调查
A census collects data from every member of the population. A sample survey collects data from only a selected part of the population. A census gives completely accurate results but is often impractical, time-consuming, and expensive. A sample survey is cheaper and quicker, but the results are estimates and may contain sampling error.
普查是收集总体中每一个成员的数据。抽样调查则只收集总体中选定部分的数据。普查能给出完全准确的结果，但通常不切实际、耗时且昂贵。抽样调查更便宜、更快捷，但结果是估计值，可能含有抽样误差。
3. Random Sampling Methods | 随机抽样方法
Simple random sampling gives every member of the population an equal chance of being selected, often using random number generators. Systematic sampling selects members at regular intervals from an ordered list, e.g. every 10th name. Stratified sampling divides the population into distinct groups (strata) and takes a random sample from each stratum proportional to its size. All these methods aim to reduce bias.
简单随机抽样让总体中每个成员都有相等的被选中机会，常借助随机数生成器。系统抽样从有序列表中按固定间隔选取成员，例如每隔 10 个名字选一个。分层抽样将总体分为不同的组（层），然后从每一层中按与层的大小成比例抽取随机样本。这些方法都旨在减少偏差。
4. Non-Random Sampling & Bias | 非随机抽样与偏差
Quota sampling selects participants based on pre-set quotas, such as a certain number of males and females. It is not random and can introduce selection bias. Opportunity sampling (convenience sampling) uses people who are easily available, like friends or passers-by. These methods are quick but often produce biased data that does not represent the population well. Bias is a systematic error that leads to over- or under-estimation of a true value.
配额抽样根据预先设定的配额选取参与者，例如一定数量的男性和女性。它并非随机，可能引入选择偏差。机会抽样（便利抽样）利用容易接触到的人，比如朋友或路人。这些方法快捷，但往往产生不能很好代表总体的有偏数据。偏差是一种系统误差，会导致对真实值的高估或低估。
5. Types of Data: Qualitative, Quantitative, Discrete, Continuous | 数据类型：定性、定量、离散、连续
Qualitative data (categorical) describes qualities or categories, like eye colour or car brand. Quantitative data involves numbers and can be measured. Discrete data can only take specific, separate values, often counts (e.g. number of siblings: 0, 1, 2, …). Continuous data can take any value within a range, like height (162.3 cm) or time (2.54 s). Knowing the data type helps choose the right chart and summary statistic.
定性数据（类别数据）描述品质或类别，如眼睛颜色或汽车品牌。定量数据涉及数字，可以被测量。离散数据只能取特定的、分离的值，通常是计数（例如兄弟姐妹数量：0, 1, 2, …）。连续数据在一个范围内可以取任意值，如身高（162.3 厘米）或时间（2.54 秒）。了解数据类型有助于选择合适的图表和汇总统计量。
6. Measures of Central Tendency: Mean, Median, Mode | 集中趋势量数：平均数、中位数、众数
The mean (x̄) is the arithmetic average: sum of all values divided by the number of values. It uses every data point and is sensitive to outliers. The median is the middle value when data is ordered; it is not affected by extreme values. The mode is the most frequently occurring value. In a frequency table, the modal class is the interval with the highest frequency. For skewed data, the median is often a better measure of location.
平均数（x̄）是算术平均值：所有数值之和除以数值个数。它使用了每一个数据点，对异常值敏感。中位数是将数据排序后中间的那个值；它不受极端值的影响。众数是出现次数最多的值。在频数表中，众数组是频数最高的区间。对于偏斜数据，中位数通常是一个更好的位置量数。
7. Measures of Spread: Range, IQR, Variance & Standard Deviation | 离散程度量数：极差、四分位距、方差与标准差
The range is the difference between the maximum and minimum values. The interquartile range (IQR) = Q₃ – Q₁, the range of the middle 50% of the data. Variance (σ²) measures the average squared deviation from the mean. Standard deviation (σ) is the square root of variance, giving a measure of spread in the original units. For a sample, we divide by (n – 1) to get an unbiased estimate of population variance.
极差是最大值与最小值的差。四分位距（IQR） = Q₃ – Q₁，是数据中间 50% 的范围。方差（σ²）衡量的是各数据与平均数离差平方的平均值。标准差（σ）是方差的正平方根，给出以原始单位表示的离散程度。对于样本，我们除以 (n – 1) 以获得总体方差的无偏估计。
8. Correlation & Regression Terminology | 相关与回归术语
Correlation describes the strength and direction of a linear relationship between two variables. Positive correlation means as one variable increases, the other tends to increase. Negative correlation means one increases while the other decreases. The product moment correlation coefficient (r) ranges from -1 to 1. Regression line (y = a + bx) is used to model the relationship; the slope b represents the change in y for a one-unit increase in x. Interpolation is predicting inside the data range, extrapolation is predicting outside, which is less reliable.
相关描述两个变量之间线性关系的强度和方向。正相关意味着一个变量增加，另一个也倾向增加。负相关意味着一个增加而另一个减少。积矩相关系数（r）取值范围在 -1 到 1 之间。回归直线（y = a + bx）用于建模这种关系；斜率 b 表示 x 每增加一个单位，y 的变化量。内插是在数据范围内进行预测，外推是在数据范围外预测，后者可靠性较低。
9. Probability Basics: Experiment, Outcome, Event | 概率基础：试验、结果、事件
An experiment is a repeatable process that gives observations. An outcome is a single possible result. An event is a set of one or more outcomes. If all outcomes are equally likely, probability = number of favourable outcomes / total number of outcomes. The sample space is the set of all possible outcomes. Mutually exclusive events cannot happen at the same time; for them, P(A ∪ B) = P(A) + P(B).
试验是一个可重复并且会产生观测结果的过程。结果是单个可能的结果。事件是一个或多个结果的集合。如果所有结果等可能，概率 = 有利结果数 / 总结果数。样本空间是所有可能结果的集合。互斥事件不能同时发生；对于互斥事件，P(A ∪ B) = P(A) + P(B)。
10. Venn Diagrams & Probability Notation | 维恩图与概率符号
A Venn diagram shows sets and their relationships. The rectangle represents the sample space, circles represent events. Intersection (A ∩ B) is the set of outcomes in both A and B. Union (A ∪ B) is the set of outcomes in A or B or both. Complement (A’) is everything not in A. The formula P(A ∪ B) = P(A) + P(B) – P(A ∩ B) handles non-mutually exclusive events. Conditional probability P(A|B) is the probability of A given that B has occurred: P(A|B) = P(A ∩ B) / P(B).
维恩图展示集合及其关系。矩形代表样本空间，圆代表事件。交集（A ∩ B）是既在 A 中又在 B 中的结果的集合。并集（A ∪ B）是在 A 或 B 或两者兼有的结果的集合。补集（A’）是所有不在 A 中的结果。公式 P(A ∪ B) = P(A) + P(B) – P(A ∩ B) 用于处理非互斥事件。条件概率P(A|B) 是在事件 B 已发生的条件下事件 A 发生的概率：P(A|B) = P(A ∩ B) / P(B)。
11. Statistical Distributions: Binomial & Normal | 统计分布：二项分布与正态分布
A binomial distribution X ~ B(n, p) models the number of successes in n independent trials, each with probability p of success. Conditions: fixed number of trials, two possible outcomes per trial, constant probability, and independence. The normal distribution X ~ N(μ, σ²) is a continuous, bell-shaped curve defined by mean μ and variance σ². About 68% of data lie within μ ± σ, 95% within μ ± 2σ. The standard normal distribution Z ~ N(0, 1²) is used to find probabilities via z-scores: z = (x – μ)/σ.
二项分布 X ~ B(n, p) 描述在 n 次独立试验中成功的次数，每次试验成功概率为 p。条件：固定试验次数、每次试验有两种可能结果、概率恒定、试验独立。正态分布 X ~ N(μ, σ²) 是一个由均值 μ 和方差 σ² 定义的连续、钟形曲线。大约 68% 的数据落在 μ ± σ 内，95% 落在 μ ± 2σ 内。标准正态分布 Z ~ N(0, 1²) 用于通过 z 值查表求概率：z = (x – μ)/σ。
12. Hypothesis Testing: Key Terms | 假设检验：关键术语
A hypothesis test assesses evidence to decide between two statements. The null hypothesis (H₀) is the assumption being tested, often a statement of ‘no effect’ or ‘no difference’. The alternative hypothesis (H₁) is what we suspect might be true. The significance level (α) is the probability of rejecting H₀ when it is true (e.g. 5%). A test statistic is calculated from the sample data. The p-value is the probability of obtaining a result at least as extreme as the observed one, assuming H₀ is true. If p < α, we reject H₀; if p > α, we do not reject H₀. The critical region is the set of values of the test statistic that leads to rejection of H₀.
假设检验评估证据以在两个陈述之间做出决定。原假设（H₀）是被检验的假设，常是“无效应”或“无差异”的陈述。备择假设（H₁）是我们怀疑可能为真的内容。显著性水平（α）是当原假设为真时拒绝它的概率（例如5%）。检验统计量由样本数据计算得出。p 值是假定原假设为真的情况下，得到至少与实际观测一样极端的结果的概率。如果 p < α，我们拒绝 H₀；如果 p > α，我们不拒绝 H₀。拒绝域是检验统计量中导致拒绝 H₀ 的取值集合。
Published by TutorHao | Statistics Revision Series | aleveler.com
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