📚 Year 12 Edexcel Statistics: Key Terminology Quick Memorisation Guide | Year 12 Edexcel 统计：词汇术语速记指南
Mastering statistical terminology is the first step towards achieving a high grade in the Edexcel Year 12 Statistics paper. Without a solid vocabulary, you risk misinterpreting questions and losing marks. This quick guide organises essential terms by topic and offers clear, bilingual explanations to help you memorise them efficiently.
掌握统计术语是Edexcel Year 12统计考试取得高分的第一步。没有扎实的词汇基础，你可能会误解题意而失分。这份快速指南按主题整理了核心术语，并提供清晰的双语解释，助你高效记忆。
1. Population and Sample | 总体与样本
Population is the entire set of individuals or items you want to investigate. It can be finite (a class of 30 students) or infinite (all possible tosses of a coin).
总体是你想要调查的全部个体或项目的集合。它可以是有限的（如一个30人的班级）或无限的（如投掷硬币的所有可能结果）。
A sample is a subset of the population selected to represent the whole. Conclusions about the population are drawn from the sample.
样本是从总体中选出的一个子集，用以代表整体。有关总体的结论是从样本中推断出来的。
A census collects data from every member of the population. It is fully accurate but often impractical, costly and time-consuming.
普查从总体的每个成员那里收集数据。它完全准确，但通常不切实际、昂贵且耗时。
Sampling frame is a list of all members of the population from which a sample is drawn. An incomplete sampling frame can introduce bias.
抽样框是总体所有成员的名单，样本从中抽取。不完整的抽样框会引入偏倚。
Bias occurs when a sample does not fairly represent the population, leading to systematic errors in conclusions.
偏倚发生在样本不能公平地代表总体时，会导致结论的系统性错误。
Memory trick: 'Census tries to Catch Everyone'. 'Frame is the filter before you draw'.
记忆窍门：'普查试图抓住每个人'。'抽样框是你抽取样本前的名单过滤器'。
2. Sampling Methods | 抽样方法
Five key sampling methods appear in Edexcel Year 12. Each has distinct advantages and drawbacks.
Edexcel Year 12涉及五种主要抽样方法，各有其独特的优缺点。
| Method | English Description | 中文描述 |
|---|---|---|
| Simple Random Sample | Every member has an equal chance of selection, using random number generators or lottery. Free of bias but needs a full sampling frame. | 简单随机抽样：每个成员被选中的机会均等，用随机数或抽签实现。无偏倚，但需要完整的抽样框。 |
| Stratified Sample | Population is divided into mutually exclusive strata (e.g. age groups), and a random sample is taken from each stratum proportionally. It guarantees representation of all groups. | 分层抽样：将总体分成互斥的层（如年龄段），然后从每层按比例随机抽样。它能保证所有群体都被代表。 |
| Systematic Sample | Choose every kth member from the sampling frame after a random starting point. Quick and simple, but can introduce periodicity bias. | 系统抽样：从抽样框中随机起点后，每隔k个成员选取一个。快速简单，但可能产生周期偏倚。 |
| Quota Sample | Interviewer selects a preset number of people with specific characteristics. Non-random; may be biased but practical when no sampling frame exists. | 配额抽样：访问员按预设数量选取具有特定特征的人。非随机，可能有偏倚，但在没有抽样框时很实用。 |
| Opportunity Sample | Select individuals who are easiest to reach (e.g. people walking by). Convenient but likely biased. | 机会抽样：选取最容易接触到的个体（如路过的人）。方便但很可能有偏倚。 |
Memory shortcut: 'Stratified has Strata', 'Quota is like filling Quota sheets', 'Systematic picks every kth like a System'.
记忆口诀：'分层有层'、'配额像填配额表'、'系统按间隔选，像一个系统'。
3. Data Types | 数据类型
Correctly identifying data types is essential for choosing appropriate diagrams and calculations.
正确识别数据类型对于选择合适的图表和计算至关重要。
- Quantitative data – numerical data that can be measured or counted. 定量数据 – 可测量或计数的数值型数据。
- Qualitative data – non-numerical data describing qualities or categories. 定性数据 – 描述性质或类别的非数值型数据。
- Discrete data – quantitative data that takes only specific, separate values (e.g. number of books, shoe size 6,7,8). 离散数据 – 只能取特定、分离值的定量数据（如书本数量、鞋码6,7,8）。
- Continuous data – quantitative data that can take any value in a given range (e.g. height, time). 连续数据 – 在给定范围内可取任意值的定量数据（如身高、时间）。
- Categorical data – qualitative data that can be sorted into categories (e.g. eye colour). 分类数据 – 可归入不同类别的定性数据（如眼睛颜色）。
- Ordinal data – qualitative data with a natural order but no precise numerical differences (e.g. satisfaction rating: poor, good, excellent). 有序数据 – 有自然顺序但无数值差异精确度的定性数据（如满意度评级：差、好、优秀）。
Think: Discrete is like counting fingers; Continuous is like measuring time. 想象：离散像数手指；连续像测量时间。
4. Measures of Central Tendency | 集中趋势的度量
Central tendency tells us about the 'middle' of the data. Three main measures appear in every exam.
集中趋势告诉我们数据的“中心”在哪里。每次考试都会出现三种主要度量。
Mean (average): the sum of all data values divided by the number of values. For raw data, x̄ = Σx / n. For grouped data, we use midpoints and frequencies.
平均数（均值）：所有数据值之和除以数据个数。对于原始数据，x̄ = Σx / n。对于分组数据，我们使用组中值与频数。
Median: the middle value when data are ordered. For n data points, the median is at position (n+1)/2. It is unaffected by extreme values.
中位数：数据排序后位于中间的值。对于n个数据点，中位数的位置在(n+1)/2。它不受极端值影响。
Mode: the most frequently occurring value or class. A data set can have no mode, one mode (unimodal) or multiple modes.
众数：出现频率最高的值或类别。一组数据可能没有众数，有一个众数（单峰）或多个众数。
When to use: Mean uses all data but is sensitive to outliers. Median is robust for skewed distributions. Mode is best for categorical data.
使用时机：均值使用所有数据，但对异常值敏感。中位数对于偏态分布稳健。众数最适合分类数据。
Estimated mean for grouped data: x̄ ≈ (Σ f xmid) / Σ f
分组数据估算均值：x̄ ≈ (Σ f xmid) / Σ f
5. Measures of Spread | 离散程度的度量
Spread tells us how consistent or varied the data are. Low spread means values are close together.
离散程度告诉我们数据的变异性或一致性。低离散度意味着数值紧密聚集。
Range = Largest value – Smallest value. Simple but heavily affected by outliers.
极差 = 最大值 – 最小值。简单但极易受异常值影响。
Interquartile range (IQR) = Upper quartile Q₃ – Lower quartile Q₁. Represents the spread of the middle 50% and is resistant to outliers.
四分位距 (IQR) = 上四分位数 Q₃ – 下四分位数 Q₁。表示中间50%数据的离散度，且抗异常值。
Variance measures average squared deviation from the mean. For a data set, variance = (Σ(x – x̄)²)/n = Σx²/n – (x̄)².
方差测量数据与均值偏差平方的平均值。对于数据集，方差 = (Σ(x – x̄)²)/n = Σx²/n – (x̄)²。
Standard deviation (σ or s) is the square root of variance, giving spread in the original units.
标准差 (σ 或 s) 是方差的平方根，以原始单位表示离散程度。
Outlier: A value that lies far from the main body of data. Commonly defined as any value below Q₁ – 1.5×IQR or above Q₃ + 1.5×IQR.
异常值：远离数据主体的值。通常定义为小于 Q₁ – 1.5×IQR 或大于 Q₃ + 1.5×IQR 的值。
Variance formula: σ² = (Σx²)/n – (x̄)²
方差公式：σ² = (Σx²)/n – (x̄)²
6. Data Representation | 数据表示
You must be able to read and construct box plots, histograms and cumulative frequency diagrams.
你必须能读并会画箱线图、直方图和累积频数图。
Box plot (box-and-whisker diagram) shows minimum, Q₁, median, Q₃ and maximum. It identifies skewness and outliers.
箱线图（盒须图）显示最小值、Q₁、中位数、Q₃和最大值。它能识别偏态和异常值。
Histogram: used for continuous data. The vertical axis is frequency density, calculated as frequency ÷ class width. The area of each bar is proportional to frequency.
直方图：用于连续数据。纵轴为频数密度，即频数 ÷ 组距。每个条形的面积与频数成正比。
Frequency density / Class width. This ensures tall narrow classes and wide flat classes are compared fairly.
频数密度 = 频数 / 组距。这样就能公平比较高窄的组与宽平的组。
Cumulative frequency graph: total frequency up to each upper class boundary. Median and quartiles can be read directly from the curve.
累积频数图：到每个上组界为止的总频数。中位数和四分位数可直接从曲线上读取。
Remember: 'Histogram height is Frequency Density, not frequency.' 记住：'直方图高度是频数密度，而非频数'。
7. Correlation and Regression | 相关与回归
Correlation measures the strength and direction of a linear relationship between two variables.
相关衡量两个变量之间线性关系的强度和方向。
Published by TutorHao | Year 12 统计 Revision Series | aleveler.com更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图