📚 SQA Statistics Vocabulary Quick-Memory Guide | SQA 统计词汇速记指南
Mastering statistical vocabulary is one of the fastest routes to higher exam marks in the SQA Statistics course. Many questions simply ask you to define a term, recognise a concept, or choose the correct word to fill a blank. This guide gives you clear English definitions, direct Chinese translations, and memorable memory hooks for the most tested terms, so you can recall them quickly under pressure.
掌握统计学术语是提高 SQA 统计课程考试成绩的捷径之一。很多题目无非是要求你定义一个术语、识别一个概念或者选词填空。本指南为你整理了最高频的考点术语，配有清晰的英文定义、中文翻译和好记的记忆钩子，让你在考试压力下也能快速回忆。
1. Population vs Sample | 总体与样本
The population is the entire group you want to draw conclusions about. Think 'P' for 'Population' = 'Pool of everyone'.
总体 (Population) 是你想要得出结论的整个群体。记住 'P' 代表 Population 也暗示 'Pool of everyone'（所有人的池子）。
The sample is a subset of the population that you actually collect data from. Think 'S' for 'Sample' = 'Selection'.
样本 (Sample) 是你实际收集数据的那部分个体，是总体的一个子集。记住 'S' 代表 Sample 也暗示 'Selection'（挑选出来的部分）。
Memory hook: Population is the whole pie, sample is the slice you taste.
记忆联想: 总体是整个派，样本是你品尝的那一片。
2. Parameter vs Statistic | 参数与统计量
A parameter is a numerical summary describing a population. It is a fixed but usually unknown value. Link 'Pa' in 'Parameter' with 'Parent population'.
参数 (Parameter) 是描述总体的数字概括，是一个固定但通常未知的数值。把 'Pa' 联想成 'Parent population'（父总体），帮助记忆参数属于总体。
A statistic is a numerical summary calculated from a sample. It varies from sample to sample. Link 'Sta' in 'Statistic' with 'Sample statistic'.
统计量 (Statistic) 是从样本计算出来的数字概括，会随样本不同而变化。把 'Sta' 联想成 'Sample statistic'。
Memory hook: Parameter → Population; Statistic → Sample. Practise saying 'P for P, S for S'.
记忆联想: 参数配总体，统计量配样本。 反复默念 'P 对 P，S 对 S'。
3. Types of Data: Categorical vs Numerical | 数据类型：分类数据与数值数据
Categorical (qualitative) data represent characteristics or labels. They are further divided into nominal (no order, like eye colour) and ordinal (natural order, like satisfaction ratings). Think: 'Nominal = Name only'; 'Ordinal = Ordered numbers'.
分类（定性）数据 表示特征或标签。可细分为 名义数据 (Nominal)（没有顺序，如眼睛颜色）和 有序数据 (Ordinal)（有天然顺序，如满意度评分）。记忆法：'Nominal' 像 'Name only'（只有名字）；'Ordinal' 像 'Ordered numbers'（有顺序的数字）。
Numerical (quantitative) data are numbers and come as discrete (countable, e.g. number of students) or continuous ete = distinct steps, like stair steps; Continuous = on a continuum, like a sliding scale.
数值（定量）数据 是数字，分为 离散型 (Discrete)（可数，如学生人数）和 连续型 (Continuous)（可测量，如身高）。离散像一级级台阶，连续像没有断点的滑动尺。
Quick table:
| Data type | Subtype | Quick clue |
| Categorical | Nominal | Name only, no order |
| Categorical | Ordinal | Order matters |
| Numerical | Discrete | Counted, whole numbers |
| Numerical | Continuous | Measured, can take any value |
4. Measures of Central Tendency | 集中趋势的度量
The mean is the arithmetic average: sum of values divided by the count. Formula:
x̄ = Σxᵢ / n
The median is the middle value when data are sorted. It is resistant to outliers — think 'median strips on a motorway keep you in the middle'.
中位数 (Median) 是排序后中间的值。它对异常值不敏感——联想 'Median strips'（公路中央分隔带）让你保持在中间。
The mode is the most frequent value. Remember 'Mode = Most often'.
众数 (Mode) 是出现次数最多的值。记住 'Mode' 像 'Most'（最多）。
Memory hook for skewed data: In a right‑skewed distribution, mean > median > mode; the tail pulls the mean. In a left‑skewed distribution, mean < median < mode.
偏态分布记忆: 右偏时平均数 > 中位数 > 众数，尾部把平均数拉高；左偏时平均数 < 中位数 < 众数。
5. Measures of Spread | 离散程度的度量
Range = maximum – minimum. It is the simplest measure of variability but easily affected by outliers.
极差 (Range) = 最大值 – 最小值。最简单的变异性度量，但极易受异常值影响。
The interquartile range (IQR) = Q₃ – Q₁. It gives the spread of the middle 50% and is robust to outliers. Think: 'IQR ignores the extremes'.
四分位距 (IQR) = 上四分位数 – 下四分位数。反映中间 50% 数据的散布，不受极端值影响。记：'IQR 忽 extremes 端'。
Variance s the average of the squared deviations from the mean. For a population, variance σ² = Σ(x – μ)² / N; for a sample, s² = Σ(x – x̄)² / (n – 1).
方差 (Variance) 是各数据与均值之差的平方的平均数。总体方差 σ² = Σ(x – μ)² / N；样本方差 s² = Σ(x – x̄)² / (n – 1)。
Standard deviation he is the square root of the variance and brings the unit back to the original data scale. Think: 'Standard deviation = Square root of variance'.
标准差 (Standard deviation) 是方差的平方根，单位与原始数据一致。记：'标准差 = 方差的平方根'。
Memory trick for n–1: You lose one degree of freedom when you estimate the mean from the sample itself, hence divide by n–1.
n–1 记忆: 你用样本估计均值时消耗了一个自由度，所以分母是 n–1。
6. Probability Basics | 概率基础
An outcome is a single possible result of a trial. The sample space is the set of all possible outcomes. The probability of an event A is P(A).
结果 (Outcome) 是一次试验可能出现的单个结果。样本空间 (Sample space) 是所有可能结果的集合。事件 A 的概率记作 P(A)。
Probability ranges from 0 (impossible) to 1 (certain). Remember the probability line: 0 ———— 0.5 ———— 1.
概率取值从 0（不可能）到 1（必然）。想象一条概率线：0 ———— 0.5 ———— 1。
Two events are mutually exclusive if they cannot happen at the same time. The key formula: P(A or B) = P(A) + P(B).
如果两个事件不能同时发生，它们就是互斥 (Mutually exclusive) 的。核心公式：P(A 或 B) = P(A) + P(B)。
Events are independent ot if the occurrence of one does not affect the probability of the other. The multiplication rule: P(A and B) = P(A) × P(B).
如果一个事件的发生不影响另一个事件发生的概率，则它们相互独立 (Independent)。乘法法则：P(A 且 B) = P(A) × P(B)。
Memory aid: 'Mutually Exclusive = ME = they can’t Mix'; 'Independent = IN = one does not Influence the other'.
记忆: 'Mutually Exclusive' 含 'Ex'，即排斥，不能混合；'Independent' 含 'in'，不依赖。
7. Conditional Probability | 条件概率
Conditional probability is the probability of event A given that event B has occurred, written as P(A | B). The formula: P(A | B) = P(A and B) / P(B).
条件概率 (Conditional probability) 是在事件 B 发生的条件下事件 A 发生的概率，记作 P(A | B)。公式：P(A | B) = P(A 且 B) / P(B)。
Visualise a Venn diagram: conditional probability is the fraction of the B circle that is also in A. 'Given' means the sample space has shrunk to B.
用韦恩图理解：条件概率就是 B 圆内同时也属于 A 的那一部分比例。'给定 (Given)' 意味着样本空间缩小到了 B。
Common exam mistake: confusing P(A | B) with P(B | A). Always check which event is the condition.
常见考试错误: 混淆 P(A | B) 和 P(B | A)。一定要看清哪个事件是条件。
8. Probability Distributions | 概率分布
A probability distribution describes the probabilities of all possible outcomes. For discrete random variables we list probabilities (sum = 1). For continuous ones we use a probability density function (area under the curve = 1).
概率分布 (Probability distribution) 描述所有可能结果的概率。对离散随机变量，我们列出各个取值的概率（总和为1）。对连续随机变量，使用概率密度函数（曲线下总面积 = 1）。
In SQA courses, three distributions dominate: Binomial (fixed number of independent trials, two outcomes, constant success probability p), Normal (bell‑shaped, symmetric, defined by μ and σ), and sometimes Poisson (counts of rare events).
SQA 课程中重点考三种分布：二项分布 (Binomial)（固定次数独立试验，两种结果，成功概率 p 恒定）、正态分布 (Normal)（钟形、对称，由 μ 和 σ 决定），有时也考泊松分布 (Poisson)（稀有事件的计数）。
Binomial memory: 'Bi' means two outcomes (success/failure) and you need a 'n' and a 'p'. Think: 'BINS' — Binary, Independent, Number fixed, Same probability.
二项分布记忆: '二' 表示两种结果（成功/失败），需要 n 和 p。记住单词 'BINS'：Binary（二元）、Independent（独立）、Number fixed（次数固定）、Same p（相同概率）。
Normal memory: The bell‑shaped curve is symmetric about the mean μ. 68% of data within 1σ, 95% within 2σ, 99.7% within 3σ — the 68‑95‑99.7 rule.
正态分布记忆: 钟形曲线关于均值 μ 对称。68% 的数据落在 μ±1σ 内，95% 在 μ±2σ 内，99.7% 在 μ±3σ 内——68-95-99.7 规则。
9. Correlation & Regression | 相关与回归
Correlation linear relationship between two variables. The correlation coefficient r is always between –1 and +1. 'r close to 1' = strong positive; 'r close to –1' = strong negative; 'r near 0' = weak or no linear relationship.
相关 (Correlation) 度量两个变量之间线性关系的强度和方向。相关系数 r 始终在 –1 到 +1 之间。r 接近 1 表示强正相关，接近 –1 表示强负相关，接近 0 表示弱线性关系或无线性关系。
Regression finds the line of best fit, often using the least‑ a + bx, where b is the slope and a is the intercept. Correlation does not imply causation!
回归 (Regression) 寻找最佳拟合直线，常用最小二乘法。方程为 y = a + bx，b 是斜率，a 是截距。注意：相关不代表因果关系！
Memory trick for slope: 'b' is the change in y per unit increase in x. Think 'b for boost'. Intercept 'a' is y when x = 0.
斜率记忆: b 是 x 每增加一个单位 y 的变化量，联想 'b 是 boost'。截距 a 是 x = 0 时的 y 值。
10. Hypothesis Testing: Key Terms | 假设检验：关键术语
Null hypothesis (H₀): the statement of no effect or no difference. It is the assumption we test. Think 'Null = Nothing new'.
原假设 (H₀): 宣称没有效应或没有差异的陈述，是我们检验时假设为真的命题。联想 'Null' 即 '零'、'无新事'。
Alternative hypothesis (H₁ or Hₐ): the statement we want to prove, often representing a change or difference. It is what you hope to support.
备择假设 (H₁ 或 Hₐ): 我们希望证明的陈述，通常代表有变化或差异。是研究的期望所在。
Test statistic: a value calculated from sample data used to decide whether to reject H₀. Examples: z‑statistic, t‑statistic.
检验统计量: 从样本数据计算出的一个数值，用于判断是否拒绝 H₀。例如 z 统计量、t 统计量。
p‑value: the probability of obtaining a test statistic at least as extreme as the one observed, assuming H₀ is true. Small p‑value → strong evidence against H₀.
p 值: 在原假设 H₀ 为真的条件下，得到当前检验统计量及更极端结果的概率。p 值很小 → 强烈证据反对 H₀。
Significance level (α): the threshold for rejecting H₀. Common α = 0.05. If p‑value < α, reject H₀. Think 'α is the cut‑off for how unlikely is too unlikely'.
显著性水平 (α): 拒绝 H₀ 的阈值，常用 α = 0.05。若 p 值 < α，则拒绝 H₀。联想 'α 是判定多不可能才算太不可能的截止线'。
11. Errors in Hypothesis Testing | 假设检验中的错误
Type I error: rejecting a true null hypothesis. Probability of making a Type I error equals α. Memory: 'Type I = false positive, you cry wolf when there is none'.
第一类错误 (Type I error): 原假设为真却拒绝之。犯第一类错误的概率等于 α。记法：'第一类 = 假阳性，明明没有狼却喊狼来了'。
Type II error: failing to reject a false null hypothesis. Probability denoted β. Memory: 'Type II = false negative, missing the wolf when it is really there'.
第二类错误 (Type II error): 原假设为假却没有拒绝。概率记作 β。记法：'第二类 = 假阴性，狼真的来了却没发现'。
Power: the probability of correctly rejecting a false H₀. Power = 1 – β. High power is desirable. To remember: 'Power = 1 – β, the ability to detect an effect'.
检验力 (Power): 当 H₀ 为假时正确拒绝它的概率。Power = 1 – β。高检验力是我们所希望的。联想：'Power 就是 1 – β，检测出效应的能力'。
Visual aid: imagine a signal detection problem — Type I is false alarm, Type II is miss. You can trade off between them but can't eliminate both without more data.
图像记忆: 想象一个信号侦测问题——第一类错误是假警报，第二类错误是漏报。二者此消彼长，要同时消除只能增加样本量。
12. Confidence Intervals | 置信区间
A confidence interval gives an estimated range of plausible values for a population parameter. A 95% confidence interval means: if we repeated the sampling many times, 95% of the calculated intervals would contain the true parameter.
置信区间 (Confidence interval) 给出总体参数一个可信值的估计范围。95% 置信区间的意思是：如果重复抽样很多次，那么 95% 的这类区间会包含真实的参数值。
General form for a mean (when σ known):
x̄ ± z* × (σ / √n)
Key components: x̄ is the sample mean, z* is the critical value (e.g. 1.96 for 95%), σ/√n is the standard error. The margin of error gets smaller with larger n.
关键组成: x̄ 是样本均值，z* 是临界值（95% 时为 1.96），σ/√n 是标准误。样本量 n 越大，误差界限越小。
Memory phrase: 'The wider the interval, the more confident you are, but the less precise.'
记忆短语: '区间越宽，越有信心，但精度越低。'
Published by TutorHao | Statistics Revision Series | aleveler.com
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