Statistical Terminology Quick-Memorising Guide | 统计术语速记指南

📚 Statistical Terminology Quick-Memorising Guide | 统计术语速记指南

Mastering the language of statistics is half the battle in SQA Year 12 Statistics. This guide breaks down key terms with simple explanations and memory tricks, helping you recall definitions accurately under exam pressure. Each term is presented in a bilingual pair so you can reinforce understanding in both English and your study language.

掌握统计学语言是征服 SQA 12 年级统计考试的一半。本指南通过简单解释和记忆技巧拆解关键术语，帮助你在考试压力下准确回忆定义。每个术语以中英双语配对呈现，让你在母语和英语中都能加深理解。

1. Types of Data | 数据类型

Data can be classified into qualitative (categorical) and quantitative (numerical) types. Qualitative data describe attributes or labels, such as favourite colour or postcode. Quantitative data arise from counting or measuring and can be discrete (countable gaps, e.g. number of pets) or continuous (any value in an interval, e.g. height). Within categorical data, nominal means ‘name only’ with no order, while ordinal implies a meaningful sequence like survey ratings.

数据可分为定性（分类）数据和定量（数值）数据。定性数据描述属性或标签，如喜爱的颜色或邮政编码。定量数据来自计数或测量，可分为离散型（有可数间隙，如宠物数量）和连续型（可在区间内取任意值，如身高）。在分类数据内部，名义数据只是”名称”，没有顺序；而有序数据有意义的排列，如调查评分等级。

Quick tip: Remember ‘Nominal = Name’ and ‘Ordinal = Order’ to distinguish them instantly. Continuous data often come from measuring instruments, discrete data from counting whole items.

速记提示：记住”Nominal = Name（名字）”、”Ordinal = Order（顺序）”可立即区分。连续数据通常来自测量仪器，离散数据来自对整件物品的计数。

2. Graphical Representations | 图表表示

Bar charts display categorical data with spaces between bars, while histograms show continuous data with touching bars and frequency density on the vertical axis. A box plot (box‑and‑whisker) summarises the five‑number summary: minimum, lower quartile, median, upper quartile, maximum. Scatter graphs reveal relationships between two numerical variables, and stem‑and‑leaf diagrams preserve original data values while grouping them.

条形图用有间隔的柱子展示分类数据，而直方图用相连的柱子呈现连续数据，纵轴为频率密度。箱线图（盒须图）概括五数综合：最小值、下四分位数、中位数、上四分位数、最大值。散点图揭示两个数值变量间的关系，茎叶图在分组时保留原始数据的值。

Memory aid: ‘Histogram height is frequency density’ – a common SQA trap is forgetting to divide frequency by class width. Stem‑and‑leaf: ‘Stem holds the tens, leaf holds the units’.

记忆辅助：”直方图高度是频率密度”——SQA 常见陷阱是忘记将频数除以组距。茎叶图：”茎存十位，叶存个位”。

3. Measures of Central Tendency | 集中趋势度量

The mean (average) is calculated as the sum of all values divided by the number of values. The median is the middle value when data are sorted; it is resistant to outliers. The mode is the most frequently occurring value. For symmetric distributions, mean ≈ median; skewed data pull the mean toward the tail.

均值（平均数）是所有值的总和除以值的个数。中位数是数据排序后的中间值；它不受异常值影响。众数是出现次数最多的值。对于对称分布，均值≈中位数；偏斜数据会把均值拉向尾部。

Formula for the population mean: μ = Σx ÷ N. The sample mean uses x̄. SQA often asks you to choose the best measure: use median for skewed data like house prices.

总体均值公式：μ = Σx ÷ N。样本均值用 x̄。SQA 常要求选择最佳度量：像房价这样的偏斜数据用中位数。

4. Measures of Dispersion | 离差度量

Range is the simplest spread measure: maximum minus minimum. Interquartile range (IQR = Q₃ – Q₁) gives the spread of the middle 50% and reduces outlier sensitivity. Variance measures average squared deviation from the mean, and standard deviation is the square root of variance, returning to the original units.

极差是最简单的离散度量：最大值减最小值。四分位距（IQR = Q₃ – Q₁）给出中间 50% 的扩展范围，降低异常值的敏感性。方差度量与均值偏差的平方平均数，标准差是方差的平方根，恢复为原单位。

Key formulas:

Population variance: σ² = Σ(x − μ)² ÷ N

Sample variance: s² = Σ(x − x̄)² ÷ (n − 1)

Standard deviation: s = √s² (use the square root). For grouped data, x represents class midpoints.

核心公式：
总体方差：σ² = Σ(x − μ)² ÷ N
样本方差：s² = Σ(x − x̄)² ÷ (n − 1)
标准差：s = √s²（求平方根）。对于分组数据，x 代表组中点。

5. Probability Vocabulary | 概率词汇

An experiment is a repeatable process with uncertain outcomes. The sample space is the set of all possible outcomes. An event is a subset of the sample space. Mutually exclusive events cannot occur together; P(A ∩ B) = 0. Independent events have no influence on each other; P(A ∩ B) = P(A) × P(B). Conditional probability P(B|A) is the probability of B given that A has occurred.

试验是可重复且结果不确定的过程。样本空间是所有可能结果的集合。事件是样本空间的子集。互斥事件不能同时发生：P(A ∩ B) = 0。独立事件互不影响：P(A ∩ B) = P(A) × P(B)。条件概率 P(B|A) 是在 A 已发生的条件下 B 发生的概率。

Conditional probability formula: P(A|B) = P(A ∩ B) ÷ P(B). To check independence, compare P(A|B) with P(A).

条件概率公式：P(A|B) = P(A ∩ B) ÷ P(B)。检查独立性时，比较 P(A|B) 与 P(A)。

6. Normal Distribution | 正态分布

The normal distribution is a symmetric, bell‑shaped curve defined by its mean μ and standard deviation σ. The standard normal distribution Z ~ N(0,1) has mean 0 and SD 1. The 68‑95‑99.7 rule states that approximately 68% of data lie within 1σ of the mean, 95% within 2σ, and 99.7% within 3σ.

正态分布是以均值 μ 和标准差 σ 为参数的对称钟形曲线。标准正态分布 Z ~ N(0,1) 均值为 0，标准差为 1。68‑95‑99.7 规则指出：约 68% 数据落在均值 ±1σ 内，95% 在 ±2σ 内，99.7% 在 ±3σ 内。

The z‑score formula: Z = (X − μ) ÷ σ. This standardises any normal observation, allowing probability calculations using the Z‑table. In SQA, you must also perform reverse look‑ups to find the original value X given a probability.

z 分数公式：Z = (X − μ) ÷ σ。它将任意正态观测值标准化，可利用 z 表计算概率。在 SQA 中，你还必须进行反向查表，根据给定概率求原值 X。

7. Correlation and Regression | 相关与回归

Correlation measures the strength and direction of a linear relationship between two variables. The product‑moment correlation coefficient r ranges from −1 to +1. r = 0 indicates no linear correlation. Remember: correlation does not imply causation. Regression finds the line of best fit, typically y = a + bx, where b is the slope and a is the intercept.

相关度量两个变量间线性关系的强度和方向。积矩相关系数 r 的范围从 −1 到 +1。r = 0 表示无线性相关。记住：相关不意味着因果关系。回归寻找最佳拟合线，通常形式为 y = a + bx，其中 b 是斜率，a 是截距。

The least‑squares regression line minimises the sum of squared residuals. The equation of the regression line can be used to predict y from a given x, but extrapolation beyond the data range is unreliable.

最小二乘回归线使残差平方和最小。回归线方程可用于从已知 x 预测 y，但外推超出数据范围不可靠。

8. Sampling Methods | 抽样方法

Simple random sampling gives every member of the population an equal chance of selection, often using random number generators. Stratified sampling divides the population into distinct groups (strata) and samples proportionally from each, improving representativeness. Systematic sampling selects every kth individual from a list. Cluster sampling splits the population into clusters and randomly selects whole clusters. Convenience sampling uses readily available subjects, which often introduces bias.

简单随机抽样让总体中每个成员有相等机会被选中，常使用随机数生成器。分层抽样将总体分为不同组（层），并从各层按比例抽样，以提高代表性。系统抽样从列表中每隔 k 个个体抽取。整群抽样将总体分成群并随机选择整个群。便利抽样使用容易获得的样本，常引入偏差。

Beware of sampling bias: a sample that is not representative leads to conclusions that cannot be generalised. SQA questions often ask you to identify the sampling method and discuss potential bias.

谨防抽样偏倚：不具代表性的样本会导致无法推广的结论。SQA 题目常要求识别抽样方法并讨论潜在的偏倚。

9. Hypothesis Testing Terms | 假设检验术语

The null hypothesis H₀ is a statement of no effect or no difference, assumed true unless evidence suggests otherwise. The alternative hypothesis H₁ states what we suspect may be true. The significance level α (often 0.05) is the probability of rejecting H₀ when it is actually true — a Type I error. A Type II error occurs when we fail to reject a false H₀.

零假设 H₀ 陈述没有效应或没有差异，在证据反对前假定为真。备择假设 H₁ 陈述我们怀疑可能为真的情况。显著性水平 α（常为 0.05）是当 H₀ 为真时拒绝它的概率——即第一类错误（弃真）。第二类错误（存伪）发生在未能拒绝错误的 H₀ 时。

The p‑value is the probability of obtaining a test statistic at least as extreme as the one observed, assuming H₀ is true. If p ≤ α, we reject H₀. The critical region (rejection region) contains values of the test statistic that lead to rejection.

p 值是在 H₀ 为真的条件下，获得至少与实际观测一样极端的检验统计量的概率。若 p ≤ α，则拒绝 H₀。拒绝域包含导致拒绝 H₀ 的检验统计量取值。

10. Common Mistakes & Memory Aids | 常见错误与记忆口诀

(1) Don’t confuse standard deviation with standard error: standard deviation describes the spread of individual data, while standard error is the standard deviation of a sample statistic (like the mean) across repeated samples. (2) ‘Correlation ≠ causation’ remains the most repeated warning in statistics. (3) When reading box plots, remember the whiskers usually reach the minimum and maximum unless outliers are present, which are marked separately with asterisks or circles.

（1）不要混淆标准差与标准误：标准差描述个体数据的离散程度，而标准误是样本统计量（如均值）在重复抽样中的标准差。（2）”相关 ≠ 因果”是统计学重复最多的警告。（3）阅读箱线图时，记住须线通常延伸到最小值和最大值，除非存在异常值，它们会单独用星号或圆圈标记。

A memorable chant for the normal distribution: ‘1, 68; 2, 95; 3, 99.7’ – chanting these numbers helps you recall the percentages inside 1σ, 2σ, and 3σ. For probability, ‘Mutually exclusive? No overlap. Independent? No influence.’

正态分布的口诀：”1，68；2，95；3，99.7″——念诵这些数字帮你记住 1σ、2σ、3σ 内的百分比。对于概率，”互斥？不重叠。独立？不影响。”

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Statistical Terminology Quick-Memorising Guide | 统计术语速记指南