A-Level CCEA Statistics: Key Terminology Revision Guide | A-Level CCEA 统计：关键术语速记指南

📚 A-Level CCEA Statistics: Key Terminology Revision Guide | A-Level CCEA 统计：关键术语速记指南

Mastering statistical vocabulary is the first step towards confidently tackling A-Level CCEA Statistics. Without a clear grasp of the precise language used in exam questions, even the strongest mathematical skills can be derailed. This revision guide pairs every key term with its Chinese equivalent and a concise explanation, creating a bilingual memory bridge that speeds up recall. Work through each section consistently, and the terminology will become second nature.

掌握统计词汇是自信应对A-Level CCEA统计学考试的第一步。如果不能在考卷上准确理解那些精确的语言，再强的数学能力也可能跑偏。这份复习指南为每一个关键术语配上中文对照和简洁的解释，搭建起一座双语记忆桥梁，能让你更快回想起定义。坚持一个一个小节学完，术语就会成为你的第二天性。

---

1. Populations, Samples & Data Types | 总体、样本与数据类型

Population: The entire set of individuals, items or measurements that we are interested in studying. For example, all A-Level students in Northern Ireland taking CCEA Statistics.

总体：我们所希望研究的全体个体、项目或测量值的完整集合。例如，所有参加CCEA统计考试的北爱尔兰A-Level学生。

Sample: A subset of the population selected to represent it. A random sample is one where every member of the population has an equal chance of being chosen.

样本：从总体中选出的、用以代表总体的一个子集。随机样本指总体中每一个成员都有均等机会被选中。

Parameter: A numerical measure that describes a characteristic of a population, such as the population mean μ.

参数：描述总体某个特征的数值度量，例如总体均值 μ。

Statistic: A numerical measure calculated from a sample, used to estimate a population parameter. For instance, the sample mean x̄ estimates μ.

统计量：由样本计算得到的数值度量，用来估计总体参数。例如，样本均值 x̄ 用来估计 μ。

Qualitative data: Non-numerical information, often called categorical data, such as eye colour or favourite subject.

定性数据：非数值的信息，常称为分类数据，如眼睛颜色或最喜欢的科目。

Quantitative data: Numerical data that can be discrete (countable, e.g. number of siblings) or continuous (measurable, e.g. height).

定量数据：数值型数据，可以是离散的（可数，如兄弟姐妹人数）或连续的（可量测，如身高）。

---

2. Probability Essentials | 概率基础

Experiment: A repeatable process that gives rise to a set of outcomes, such as rolling a die.

试验：一个可重复的过程，会产生一组结果，例如掷一枚骰子。

Outcome: A single possible result of an experiment. For the roll of a die, the outcomes are 1, 2, 3, 4, 5 or 6.

结果：试验的一个单一可能结果。掷骰子的结果就是1,2,3,4,5或6。

Event: A set of one or more outcomes, usually denoted by a capital letter. 'Rolling an even number' is an event containing outcomes {2, 4, 6}.

事件：由一个或多个结果组成的集合，通常用大写字母表示。“掷出偶数”就是一个包含{2,4,6}的事件。

Probability (certain). P(A) = number of favourable outcomes / total number of equally likely outcomes.

概率：衡量事件发生可能性的度量，范围从0（不可能）到1（必然）。P(A) = 有利结果数 / 所有等可能结果总数。

Conditional probability e : The probability of event A occurring given that event B has already occurred, written as P(A|B). P(A|B) = P(A ∩ B) / P(B).

条件概率：已知事件B已发生的情况下事件A发生的概率，写作P(A|B)。P(A|B) = P(A ∩ B) / P(B)。

Independent events if : Two events are independent if the occurrence of one does not affect the probability of the other; mathematically P(A ∩ B) = P(A) × P(B).

独立事件：如果一个事件的发生不影响另一个事件的概率，则两者独立；数学表达为P(A ∩ B) = P(A) × P(B)。

---

3. Random Variables & Distributions | 随机变量与分布

Random variable: A variable whose value is a numerical outcome of a random phenomenon. They are usually denoted by capital letters such as X.

随机变量：其数值为随机现象的结果的变量，通常用大写字母如X表示。

Discrete random variable: A random variable that can take only a countable number of distinct values, like the score on a die.

离散随机变量：只能取可数个不同值的随机变量，例如骰子的点数。

Continuous random variable: A random variable that can take any value within an interval, such as the exact mass of an apple.

连续随机变量：在一个区间内可取任意值的随机变量，例如一个苹果的精确质量。

Probability mass function (PMF) ete X, the function P(X = x) lists the probability for each possible value x; ΣP(X=x) = 1.

概率质量函数：对于离散型X，函数P(X = x)列出了每个可能取值x的概率；∑P(X=x) = 1。

Probability density function (PDF): For a continuous X, the function f(x) is used so that the area under the curve between a and b equals P(a < X < b).

概率密度函数：对于连续型X，函数f(x)用来表示，曲线下a与b之间的面积等于P(a < X < b)。

---

4. Expectation & Variance | 期望与方差

Expected value E(X) riable. For a discrete X, E(X) = Σ x·P(X=x). For continuous X, it is found by integration.

期望值E(X)：随机变量的长期平均取值。离散型：E(X) = ∑ x·P(X=x)。连续型则通过积分求得。

Variance Var(X) of how spread out the values are around the mean. Var(X) = E[(X − μ)²] = E(X²) − [E(X)]².

方差Var(X)：衡量数据在均值附近离散程度的量。Var(X) = E[(X − μ)²] = E(X²) − [E(X)]²。

Standard deviation σ tive square root of the variance, σ = √Var(X). It has the same units as the original data.

标准差σ：方差的正平方根，σ = √Var(X)。它的单位与原始数据一致。

Linear transformation , then E(Y) = aE(X) + b and Var(Y) = a² Var(X). This is vital for standardising variables.

线性变换：若Y = aX + b，则E(Y) = aE(X) + b，Var(Y) = a² Var(X)。这条性质对变量标准化至关重要。

---

广告 / Sponsored

5. Discrete Distributions: Binomial & Poisson | 离散分布：二项与泊松

Binomial distribution B(n, p): Models the number of successes in n independent trials, each with success probability p. X ~ B(n, p).

二项分布B(n, p)：对n次独立试验中成功的次数建模，每次成功概率为p。记为X ~ B(n, p)。

P(X = r) = ⁿC_r p^r (1 − p)^n−r

P(X = r) = C(n, r)·p^r(1 − p)^n−r

Poisson distribution Po(λ): Models the number of events occurring in a fixed interval when events happen at a constant average rate λ and are independent. X ~ Po(λ).

泊松分布Po(λ)：在固定区间内，事件以恒定平均速率λ发生且各事件相互独立时，对事件发生次数的建模。X ~ Po(λ)。

P(X = r) = e^−λ λ^r / r!

P(X = r) = e^−λ·λ^r / r!

Conditions for binomial: Fixed n; trials independent; two outcomes per trial; constant p. 'BINS': Binary, Independent, Number fixed, Same probability.

二项分布条件：固定n；各次试验独立；每次试验两种结果；p恒定。记忆口诀“BINS”：二元结果(Binary)、独立(Independent)、固定次数(Number)、相同概率(Same probability)。

Conditions for Poisson: Events occur singly, at a constant rate, independently, in a given interval. 'RISC': Random, Independent, Single (no simultaneous events), Constant rate.

泊松分布条件：事件在给定区间内单个发生、速率恒定且相互独立。记忆“RISC”：随机(Random)、独立(Independent)、单个(Single)、恒定速率(Constant)。

---

6. The Normal Distribution | 正态分布

Normal distribution N(μ, σ²): A continuous distribution with a bell-shaped curve, symmetric about the mean μ. The spread is described by variance σ².

正态分布N(μ, σ²)：具有钟形曲线的连续分布，关于均值μ对称。离散程度由方差σ²描述。

Z = (X − μ) / σ ~ N(0, 1)

Z = (X − μ) / σ ~ N(0, 1)

Standard normal distribution stribution with mean 0 and variance 1. Any normal variable can be standardised using the Z‑score. Tables give Φ(z) = P(Z ≤ z).

标准正态分布：均值为0、方差为1的分布。任何正态变量都可以通过Z分数标准化。标准正态表给出Φ(z) = P(Z ≤ z)。

Empirical rule (68‑95‑99.7%): In a normal distribution, about 68% of data lie within ±1σ of μ, 95% within ±2σ, and 99.7% within ±3σ.

经验法则（68‑95‑99.7%）：在正态分布中，约68%的数据落在μ ± 1σ内，95%落在μ ± 2σ内，99.7%落在μ ± 3σ内。

InvNorm / backward normal p. This requires the inverse normal function or reading standard normal tables in reverse.

逆正态：给定概率p，找到值k使得P(X < k) = p。需要用逆正态函数或反向查标准正态表。

---

7. Sampling & the Central Limit Theorem | 抽样与中心极限定理

Sampling distribution: The probability distribution of a statistic, such as the sample mean. It describes how the statistic varies from sample to sample.

抽样分布：某个统计量（如样本均值）的概率分布。它描述了该统计量在反复抽样中的变动规律。

Central Limit Theorem (CLT) 30), the sampling distribution of the sample mean is approximately normal, regardless of the population's shape. The mean of X̄ is μ and its variance is σ²/n.

中心极限定理：当样本量n足够大（通常n ≥ 30）时，不论总体形状如何，样本均值的抽样分布都近似正态。X̄的均值为μ，方差为σ²/n。

X̄ ~ N(μ, σ²/n) approximately

X̄ ~ N(μ, σ²/n) 近似成立

Standard error: The standard deviation of a sampling distribution. For the sample mean, SE = σ/√n. It measures the precision of the estimate.

标准误差：抽样分布的标准差。对于样本均值，SE = σ/√n。它衡量估计量的精准程度。

---

8. Confidence Intervals | 置信区间

Confidence interval: An interval of values calculated from sample data that is believed to contain the unknown population parameter with a certain level of confidence, e.g. 95%.

置信区间：根据样本数据计算出的一个数值区间，相信该区间以一定置信水平（如95%）包含未知的总体参数。

95% confidence interval for μ (σ known): x̄ ± 1.96 × σ/√n. The multiplier 1.96 comes from the standard normal distribution (z_0.025).

σ已知时μ的95%置信区间：x̄ ± 1.96 × σ/√n。乘数1.96来自标准正态分布（z_0.025）。

x̄ ± z* × σ/√n

x̄ ± z* × σ/√n

Interpretation: If we were to take many samples and construct a 95% CI each time, 95% of those intervals would capture μ. It is not saying there is a 95% chance that a single interval contains μ.

解释：如果我们重复抽取许多样本并每次都构造一个95%置信区间，那么其中95%的区间会捕获μ。这并不是说某个特定区间有95%的概率包含μ。

Margin of error: The quantity z* × σ/√n (or t* × s/√n). It shows how far the estimate and the true parameter may differ due to sampling variability.

边际误差：z* × σ/√n（或t* × s/√n）的值。它反映出由于抽样波动，估计值与真实参数可能相差多远。

---

9. Hypothesis Testing & Errors | 假设检验与错误类型

Null hypothesis H₀ nt that a population parameter equals a specified value, often the status quo. H₀: μ = μ₀.

原假设H₀：陈述总体参数等于某一指定值，通常是“现状”假设。H₀: μ = μ₀。

Alternative hypothesis H₁: The statement we are looking for evidence to support, e.g. H₁: μ > μ₀ (one-tailed) or μ ≠ μ₀ (two-tailed).

备择假设H₁：我们寻找证据去支持的陈述，例如H₁: μ > μ₀（单尾）或μ ≠ μ₀（双尾）。

Significance level α of rejecting H₀ when it is actually true. Commonly α = 0.05. This is a Type I error rate.

显著性水平α：当H₀实际为真时拒绝H₀的概率。常用α = 0.05。这就是第一类错误率。

Test statistic ed value computed from the sample, used to decide whether to reject H₀. For a mean, z = (x̄ − μ₀)/(σ/√n).

检验统计量：由样本计算出的标准化值，用于决定是否拒绝H₀。对于均值，z = (x̄ − μ₀)/(σ/√n)。

p-value: The probability of obtaining a test statistic at least as extreme as the observed one, assuming H₀ is true. If p-value < α, reject H₀.

p值：在H₀为真的前提下，得到至少和观测值一样极端的检验统计量的概率。若p值 < α，则拒绝H₀。

Type I error: Rejecting a true H₀. The probability is α. Type II error: Failing to reject a false H₀. The probability is β.

第一类错误：拒绝了真实的H₀，概率为α。第二类错误：未能拒绝错误的H₀，概率为β。

Power of a test: 1 − β, the probability of correctly rejecting a false H₀.

检验功效：1 − β，即正确拒绝错误H₀的概率。

---

10. Chi-Squared Tests | 卡方检验

Chi-squared statistic χ² measure of the discrepancy between observed and expected frequencies. χ² = Σ (O − E)² / E.

卡方统计量χ²：衡量观测频数与期望频数

Published by TutorHao | A-Level 统计 Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）