📚 GCSE Cambridge Statistics: Quick Guide to Key Terms | GCSE剑桥统计：词汇术语速记指南
Mastering statistical vocabulary is essential for success in GCSE Cambridge Statistics. This guide presents key terms with clear definitions and examples, helping you memorise them quickly and apply them confidently in your exam. Each term is paired with its Chinese equivalent to support bilingual learning.
掌握统计词汇是学好GCSE剑桥统计的关键。本指南用清晰的定义和实例罗列核心术语，帮助你快速记忆并在考试中自信运用。每个术语都配以中文对应词，方便双语学习。
1. Types of Data | 数据类型
Qualitative data (categorical data) describes qualities or categories that cannot be measured numerically, such as favourite colour, type of pet, or gender.
定性数据（分类数据）描述不可用数值衡量的属性或类别，例如喜欢的颜色、宠物种类或性别。
Quantitative data consists of numerical values that can be measured or counted. It is split into discrete data (countable, e.g. number of cars) and continuous data (measurable, e.g. height, time).
定量数据由可测量或可计数的数值组成。它分为离散数据（可数的，如汽车数量）和连续数据（可测量的，如身高、时间）。
Nominal data is a type of qualitative data where categories have no natural order, such as types of fruit or colours.
名义数据是一种定性数据，其类别没有内在顺序，例如水果种类或颜色。
Ordinal data is qualitative data with a clear order or ranking, like exam grades (A, B, C) or satisfaction levels (low, medium, high).
有序数据是具有明显顺序或等级的定性数据，比如考试成绩（A, B, C）或满意度（低、中、高）。
2. Data Collection Methods | 数据收集方法
Primary data is collected directly by the researcher for a specific purpose, e.g. through surveys or experiments.
原始数据由研究者为特定目的直接收集，例如通过问卷调查或实验。
Secondary data is data that already exists and was gathered by someone else, such as government reports or internet databases.
二手数据是已经存在的、由他人收集的数据，如政府报告或网络数据库。
Census collects data from every member of the population. It gives accurate results but can be time‑consuming and expensive.
普查从总体中的每个个体收集数据。它结果准确，但费时且成本高。
Sample is a subset of the population used to estimate characteristics of the whole group. A representative sample reduces bias.
样本是总体的一部分，用来估计整体特征。有代表性的样本可减少偏差。
Questionnaire is a set of written questions used to gather opinions or facts. Questions must be clear and unbiased.
问卷是一套用于收集意见或事实的书面问题。问题必须清晰且不带偏见。
3. Measures of Central Tendency | 集中趋势度量
Mean is the average, calculated by summing all values and dividing by the number of values. For grouped data, use the midpoints of intervals.
平均数是将所有数值相加后除以数值个数得到的平均值。对于分组数据，使用组中值进行计算。
Mean x̄ = Σx / n
平均数 x̄ = Σx / n
Median is the middle value when data is ordered. If n is even, it is the mean of the two central values.
中位数是数据排序后位于中间的值。若数据个数 n 为偶数，则取中间两个数的平均数。
Mode is the most frequent value (or modal class for grouped data). A set may have no mode, one mode, or several.
众数是出现次数最多的值（对于分组数据是众数组）。一组数据可能无众数、单众数或多众数。
Weighted mean gives different importance to values, used when some data points carry more significance.
加权平均数赋予不同数值不同的重要性，用于某些数据点权重更大的情形。
4. Measures of Dispersion | 离散程度度量
Range is the difference between the largest and smallest values. It is simple but sensitive to outliers.
极差是最大值与最小值之差。它计算简单，但易受异常值影响。
Interquartile range (IQR) is the difference between the upper quartile (Q₃) and lower quartile (Q₁), representing the spread of the middle 50% of data.
四分位距 (IQR) 是上四分位数 (Q₃) 与下四分位数 (Q₁) 之差，表示中间50%数据的分散程度。
Variance measures the average squared deviation from the mean. Its square root gives the standard deviation.
方差衡量每个数值与平均数之差的平方的平均值。其平方根为标准差。
s² = Σ(x − x̄)² / (n − 1)
方差 s² = Σ(x − x̄)² / (n − 1)
Standard deviation shows how much data deviates from the mean on average. A low value means data is clustered closely around the mean.
标准差表示数据平均偏离平均数的程度。数值越小，数据越集中在平均数附近。
5. Charts and Graphs | 图表与图形
Bar chart uses rectangular bars to represent frequencies or values for distinct categories. Bars do not touch.
条形图用矩形条表示不同类别的频数或数值。条形之间不接触。
Pie chart ions as slices of a circle, each slice angle equal to (category frequency / total) × 360°.
饼图以圆形的扇形表示比例，每个扇形的角度等于（类别频数 / 总数）× 360°。
Histogram is used for continuous grouped data. The area of each bar is proportional to frequency, so frequency density is needed when class widths are unequal.
直方图用于连续分组数据。每个矩形的面积与频数成正比，当组距不等时需要使用频率密度。
Frequency polygon joins the midpoints of the tops of histogram bars with straight lines, often used to compare distributions.
频数多边形用直线连接直方图各柱顶部的组中值，常用于比较分布。
Cumulative frequency curve (ogive) plots cumulative frequency against the upper class boundary. Used to estimate quartiles and percentiles.
累积频数曲线（肩形图）将累积频数相对于组上限绘制。用于估计四分位数和百分位数。
6. Probability Basics | 概率基础
Experiment is a repeatable process that gives observable outcomes, like rolling a die.
试验是可重复并能观察到结果的过程，如掷骰子。
Outcome is a possible result of an experiment, e.g. 'heads' when flipping a coin.
结果是试验可能产生的一个结果，如抛硬币得到的'正面'。
Event is a set of one or more outcomes, e.g. rolling an even number on a die.
事件是一个或多个结果的集合，例如掷骰子得到偶数点。
Sample space is the list of all possible outcomes. For two coins it is {HH, HT, TH, TT}.
样本空间是所有可能结果的列表。掷两枚硬币的样本空间为 {正正, 正反, 反正, 反反}。
Theoretical probability favourable outcomes / total number of outcomes, assuming all outcomes are equally likely.
理论概率 = 有利结果数 / 可能结果总数，假设所有结果等可能发生。
Experimental probability (relative frequency) is based on actual trials: frequency of event / total number of trials.
实验概率（相对频率）基于实际试验：事件发生次数 / 总试验次数。
Mutually exclusive events cannot happen at the same time. P(A ∩ B) = 0.
互斥事件不能同时发生，P(A ∩ B) = 0。
Independent events: the occurrence of one does not affect the probability of the other. P(A ∩ B) = P(A) × P(B).
独立事件：一个事件的发生不影响另一个事件发生的概率。P(A ∩ B) = P(A) × P(B)。
7. Correlation and Regression | 相关与回归
Correlation describes the strength and direction of a linear relationship between two variables. It can be positive, negative, or zero.
相关描述两个变量之间线性关系的强度和方向，可以是正相关、负相关或零相关。
Positive correlation means as one variable increases, the other also tends to increase.
正相关意味着一个变量增大时另一个变量也倾向于增大。
Negative correlation means as one variable increases, the other tends to decrease.
负相关意味着一个变量增大时另一个变量倾向于减小。
Line of best fit is drawn through a scatter graph to summarise the trend, balancing points above and below the line.
最佳拟合线画在散点图上以概括趋势，使线上方和线下方的点大致平衡。
Interpolation is estimating a value within the range of the given data, which is usually reliable.
内插法是在已知数据范围内进行估值，通常比较可靠。
Extrapolation is predicting a value outside the range of the data. It can be unreliable because the trend might not continue.
外推法是预测已知数据范围之外的值。因为趋势可能不延续，所以不太可靠。
8. Sampling Techniques | 抽样技术
Random sampling gives every member of the population an equal chance of being selected, e.g. using a random number generator.
随机抽样使总体中每个成员有相等的机会被选中，如使用随机数生成器。
Stratified sampling divides the population into groups (strata) and takes a random sample proportional to the size of each stratum. It guarantees representation.
分层抽样将总体划分为多个层，并在每层中按比例随机取样，确保代表性。
Systematic sampling selects every k‑th member from a list, starting from a random point. Quick but can introduce bias if there is a hidden pattern.
系统抽样从列表上随机起点开始，每隔k个成员选一个。速度快，但若存在隐藏模式则可能引入偏差。
Quota sampling fills pre‑set quotas for certain groups; interviewers select people non‑randomly. It is cheap but prone to selection bias.
配额抽样事先设定各组配额，由调查员非随机地选取对象。成本低，但容易产生选择偏差。
Convenience sampling uses subjects who are easiest to reach, e.g. friends or nearby people. Highly biased and not representative.
便利抽样选取最易接触的对象，如朋友或附近的人。偏差很大，缺乏代表性。
Sampling frame is the list of all individuals from which a sample is drawn. Inaccuracies in the frame cause bias.
抽样框是用于抽取样本的全体成员名单。抽样框的不准确会导致偏差。
9. Statistical Distributions | 统计分布
Box‑and‑whisker plot (box plot) displays the minimum, Q₁, median, Q₃ and maximum. It clearly shows spread and identifies outliers.
箱线图（箱形图）显示最小值、下四分位数、中位数、上四分位数和最大值，清晰展示分散程度并识别异常值。
Outlier is an extreme value that lies far from the rest of the data; often defined as beyond 1.5 × IQR from the quartiles.
异常值是远离其他数据的极端值；通常定义为超出四分位数1.5倍IQR范围的数据点。
Symmetrical distribution has a mirror‑mage shape when folded at the centre. Mean = median in a perfectly symmetric distribution.
对称分布沿中心对折时呈镜像。完全对称分布中，平均数等于中位数。
Skewed distribution has a longer tail on one side. A positive skew means the tail extends to the right; negative skew extends to the left.
偏态分布一侧有较长尾部。正偏态是右侧尾部较长，负偏态是左侧尾部较长。
Normal distribution is bell‑shaped and symmetric, with data concentrated around the mean. Its properties are governed by mean and standard deviation.
正态分布呈钟形且对称，数据集中于均值附近。其性质由均值和标准差决定。
10. Statistical Enquiry Cycle | 统计调查循环
Problem: state the question clearly, specifying the population and the variables of interest.
提出问题：明确阐述问题，指定总体和感兴趣的变量。
Plan: decide how to collect data, choose sampling method, design questionnaires, and consider ethical issues.
制定计划：决定如何收集数据，选择抽样方法，设计问卷，并考虑伦理问题。
Data: collect the data according to the plan, ensuring accuracy and recording it in a suitable format.
收集数据：按照计划收集数据，确保准确性并以合适格式记录。
Analysis: process the data using graphs, summary statistics (mean, IQR, etc.) and look for patterns or relationships.
分析数据：使用图形、概括统计量（平均数、四分位距等）处理数据，寻找模式和关系。
Conclusion: interpret findings in the context of the original problem, discuss limitations, and suggest improvements.
得出结论：在原问题背景下解释发现，讨论局限性并提出改进建议。
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