📚 Year 10 Edexcel Statistics: Quick Reference Guide to Key Terms | Year 10 Edexcel 统计：词汇术语速记指南
Welcome to your quick reference guide for key statistical terms in Year 10 Edexcel Statistics. This guide pairs each essential term with a clear explanation, helping you memorise definitions and understand how to apply them in exam questions. Use these bilingual notes to reinforce your vocabulary and build confidence in data analysis, probability, and sampling.
欢迎使用这份 Year 10 Edexcel 统计重点词汇速记指南。本指南为每个核心术语配以清晰的解释，帮助你记忆定义并理解如何在考试题目中应用。利用这些中英双语笔记来巩固词汇，建立数据分析、概率和抽样方面的信心。
1. Types of Data | 数据类型
In Statistics, data is the information collected for analysis. Data can be classified into different types, and recognising each type helps you choose the right methods of display and calculation.
在统计学中，数据是为分析而收集的信息。数据可以分为不同类型，识别每种类型有助于选择正确的展示和计算方法。
Qualitative (categorical) data: data that describes qualities or characteristics and cannot be measured numerically. Examples: eye colour, favourite subject, type of transport.
定性（分类）数据：描述性质或特征、无法用数值测量的数据。示例：眼睛颜色、最喜欢的科目、交通方式。
Quantitative (numerical) data: data that represents quantities or measurements. Examples: height, test scores, temperature.
定量（数值）数据：表示数量或测量值的数据。示例：身高、测试成绩、温度。
Discrete data: quantitative data that can only take specific, separate values, usually counts. Examples: number of siblings, goals scored, shoe size.
离散数据：只能取特定、分离数值的定量数据，通常是计数。示例：兄弟姐妹数量、进球数、鞋码。
Continuous data: quantitative data that can take any value within a range, often measurements. Examples: length, time, weight.
连续数据：在某一范围内可以取任意值的定量数据，通常是测量值。示例：长度、时间、重量。
2. Measures of Central Tendency | 集中趋势的度量
Measures of central tendency describe the centre of a data set. The three main measures are the mean, median and mode.
集中趋势的度量描述数据集的中心。三种主要度量是平均值、中位数和众数。
Mode: the value that appears most frequently in a data set. A data set can have no mode, one mode (unimodal), or more than one mode (bimodal, multimodal).
众数：数据集中出现频率最高的值。数据集可以没有众数、有一个众数（单峰）或有多个众数（双峰、多峰）。
Median: the middle value when the data are arranged in order. For an even number of values, the median is the mean of the two central numbers.
中位数：将数据按顺序排列后位于中间的值。如果数据个数为偶数，中位数是中间两个数的平均值。
Mean: the sum of all data values divided by the number of values. It is often called the ‘average’.
平均值：所有数据值之和除以数据值的总个数。通常被称为“平均数”。
Mean = Sum of all data values ÷ n (n = number of values)
3. Measures of Spread | 离散程度的度量
Measures of spread tell us how spread out or consistent the data are. The range and interquartile range (IQR) are the most common measures at this level.
离散程度的度量告诉我们数据有多分散或多一致。在这个学习阶段，极差和四分位距（IQR）是最常用的度量。
Range: the difference between the highest and lowest values in the data set. It is the simplest measure of spread but can be affected by outliers.
极差：数据集中最大值与最小值的差。它是最简单的离散度量，但会受异常值影响。
Lower quartile (Q₁): the median of the lower half of the data (excluding the median if the number of data points is odd). It marks the 25th percentile.
下四分位数（Q₁）：数据下半部分的中位数（如果数据点个数为奇数，则不包括中位数）。它标记第 25 百分位数。
Upper quartile (Q₃): the median of the upper half of the data. It marks the 75th percentile.
上四分位数（Q₃）：数据上半部分的中位数。它标记第 75 百分位数。
Interquartile range (IQR): the difference between the upper and lower quartiles. It shows the spread of the middle 50% of the data and is not affected by extreme values.
四分位距（IQR）：上四分位数与下四分位数的差值。它显示中间 50% 数据的离散程度，且不受极端值影响。
Range = Maximum − Minimum
IQR = Q₃ − Q₁
4. Frequency Distributions and Charts | 频率分布与图表
Frequency distributions organise raw data into tables, and charts help us visualise the data. The type of chart depends on the data type.
频率分布将原始数据整理成表格，图表则帮助我们将数据可视化。图表的类型取决于数据类型。
Frequency table: a table that lists each data value or category alongside its frequency (the number of times it occurs).
频率表：列出每个数据值或类别及其频率（出现次数）的表格。
Grouped frequency table: used for continuous data or large discrete data sets. Data are sorted into class intervals, and the frequency for each interval is recorded.
分组频率表：用于连续数据或大型离散数据集。数据被分入组距，并记录每个区间的频率。
Bar chart: used for categorical or discrete data. The height of each bar represents the frequency, and there are gaps between bars.
条形图：用于分类或离散数据。每个条形的高度表示频率，条形之间有间隙。
Pie chart: a circular chart divided into sectors, where each sector’s angle is proportional to the frequency of the category. The total angle is 360°.
饼图：一种被分成多个扇形的圆形图表，每个扇形的圆心角与类别的频率成比例。总角度为 360°。
Histogram: used for continuous data with equal class widths. The area of each bar is proportional to the frequency. With equal widths, the height represents frequency.
直方图：用于等组距的连续数据。每个条形的面积与频率成比例。当组距相等时，高度表示频率。
Frequency density: used to draw histograms when class widths are unequal. It is calculated as frequency divided by class width.
频率密度：当组距不相等时用于绘制直方图。它等于频率除以组距。
Frequency density = Frequency ÷ Class width
5. Box Plots and Quartiles | 箱线图与四分位数
A box plot (or box-and-whisker diagram) is a graphical summary of a data set based on the five-number summary. It shows central tendency, spread and potential outliers.
箱线图（或称箱须图）是基于五数概括的数据集图形汇总。它显示集中趋势、离散程度和潜在异常值。
Five-number summary: consists of the minimum, lower quartile (Q₁), median (Q₂), upper quartile (Q₃) and maximum.
五数概括：包括最小值、下四分位数（Q₁）、中位数（Q₂）、上四分位数（Q₃）和最大值。
Box plot construction: a box is drawn from Q₁ to Q₃ with a line inside at the median. Whiskers extend to the minimum and maximum that are not outliers.
箱线图的绘制：从 Q₁ 到 Q₃ 画一个矩形箱，箱内一条线表示中位数。触须延伸到非异常值的最小值和最大值。
Outlier: an extreme value that is unusually far from the rest of the data. A common rule is that a value is an outlier if it lies more than 1.5 × IQR below Q₁ or above Q₃. Outliers are marked with a cross on a box plot.
异常值：与数据中其他部分相距异常远的极端值。常见规则是，若某值低于 Q₁ − 1.5 × IQR 或高于 Q₃ + 1.5 × IQR，则该值为异常值。箱线图中用叉号标记异常值。
6. Scatter Graphs and Correlation | 散点图与相关性
Scatter graphs display the relationship between two sets of numerical data. Understanding correlation helps us interpret patterns and make predictions.
散点图展示两组数值数据之间的关系。理解相关性有助于我们解释规律并进行预测。
Scatter graph: a graph where each pair of values from two variables is plotted as a coordinate (x, y). The pattern shows the type and strength of correlation.
散点图：将来自两个变量的每对数值以坐标 (x, y) 的形式绘制的图形。点的分布模式展示相关性的类型和强度。
Positive correlation: as one variable increases, the other tends to increase. The points slope upwards.
正相关：当一个变量增加时，另一个变量也趋于增加。点的走向向上倾斜。
Negative correlation: as one variable increases, the other tends to decrease. The points slope downwards.
负相关：当一个变量增加时，另一个变量趋于减少。点的走向向下倾斜。
No correlation: there is no clear pattern; the points are scattered randomly.
无相关：没有明显的规律，点随机散落。
Line of best fit: a straight line drawn through the centre of the data points to model the relationship. It is used to estimate unknown values (interpolation within the data range).
最佳拟合线：穿过数据点中心的一条直线，用于对关系进行建模。它可用于估算未知值（在数据范围内的内插）。
Extrapolation: extending the line of best fit beyond the existing data. It can be unreliable because the trend may not continue outside the observed range.
外推：将最佳拟合线延伸到现有数据范围之外。外推可能不可靠，因为趋势未必在观测范围外延续。
Correlation does not imply causation: just because two variables are correlated does not mean that one causes the other. External factors may be responsible.
相关不代表因果：两个变量具有相关性并不意味着一个导致了另一个。可能是外部因素造成的。
7. Probability Basics | 概率基础
Probability measures how likely an event is to happen. It is expressed as a number between 0 (impossible) and 1 (certain), or as a percentage.
概率衡量一个事件发生的可能性大小。它用 0（不可能）到 1（必然）之间的数字表示，也可用百分比表示。
Experiment: a repeatable process that produces outcomes. Examples: rolling a die, picking a card.
试验：一个可重复进行并产生结果的过程。示例：掷骰子、抽一张牌。
Outcome: a possible result of an experiment. For a fair six-sided die, the outcomes are 1, 2, 3, 4, 5, 6.
结果：试验的一种可能发生的情况。对于一枚均匀的六面骰子，结果有 1, 2, 3, 4, 5, 6。
Event: a set of one or more outcomes. ‘Rolling an even number’ is an event containing outcomes 2, 4, 6.
事件：一个或多个结果的集合。“掷出偶数点数”是一个事件，包含结果 2, 4, 6。
Theoretical probability: probability based on equally likely outcomes, calculated without performing the experiment.
理论概率：基于等可能结果，无需实际进行试验就能计算出的概率。
P(Event) = Number of favourable outcomes ÷ Total number of possible outcomes
Experimental probability (relative frequency): probability estimated by conducting an experiment or using historical data.
实验概率（相对频率）：通过进行试验或使用历史数据估算出的概率。
Relative frequency = Frequency of event ÷ Total number of trials
Probability scale: a number line from 0 to 1 where probabilities can be marked to show how likely events are.
概率标尺：一条从 0 到 1 的数轴，可在其上标记概率以显示事件的可能性大小。
8. Sample Spaces and Events | 样本空间与事件
The sample space is the set of all possible outcomes of an experiment. Organising the sample space systematically helps you find probabilities accurately.
样本空间是试验所有可能结果的集合。系统化地整理样本空间有助于准确求出概率。
Sample space: the complete list of all possible outcomes. For tossing two coins, the sample space is {HH, HT, TH, TT}.
样本空间：所有可能结果的完整清单。抛掷两枚硬币的样本空间为 {正正, 正反, 反正, 反反}。
Sample space diagram: a table or list that displays all combinations of outcomes for two events, for example when rolling two dice.
样本空间图：展示两个事件所有结果组合的表格或列表，例如掷两枚骰子的结果。
Random experiment: an experiment where all outcomes are equally likely if the equipment is fair. Fairness means no built-in bias.
随机试验：如果工具是公平的，则所有结果等可能发生的试验。公平意味着没有内在的偏向。
Biased (unfair): a probability device that does not give equally likely outcomes. A biased die might favour certain numbers.
有偏（不公平）：不产生等可能结果的概率工具。一枚有偏的骰子可能倾向于出现某些数字。
9. Probability Rules | 概率规则
When working with more than one event, you use probability rules to combine probabilities. The addition rule and multiplication rule are essential for problem solving.
当涉及多个事件时，需要使用概率规则来组合概率。加法规则和乘法规则是解题的关键。
Mutually exclusive events: events that cannot happen at the same time. For example, getting a head and a tail on a single coin toss are mutually exclusive.
互斥事件：不可能同时发生的事件。例如，掷一枚硬币时得到正面和反面是互斥的。
Addition rule for mutually exclusive events: the probability that either A or B occurs is the sum of their individual probabilities.
互斥事件的加法规则：事件 A 或 B 发生的概率等于它们各自概率之和。
If A and B are mutually exclusive, P(A or B) = P(A) + P(B)
Exhaustive events: a set of events that cover all possible outcomes. Their probabilities sum to 1. For a die, the events ‘roll an odd number’ and ‘roll an even number’ are exhaustive and mutually exclusive.
穷举事件：涵盖所有可能结果的一组事件。它们的概率之和为 1。对一枚骰子而言，“掷出奇数”和“掷出偶数”是穷举且互斥的。
Independent events: events where the outcome of one does not affect the probability of the other. For example, rolling a die and flipping a coin are independent.
独立事件：一个事件的结果不影响另一个事件概率的情况。例如，掷骰子和抛硬币是独立事件。
Multiplication rule for independent events: the probability that both A and B occur is the product of their probabilities.
独立事件的乘法规则：事件 A 和 B 同时发生的概率等于它们各自概率的乘积。
If A and B are independent, P(A and B) = P(A) × P(B)
10. Sampling Methods | 抽样方法
In Statistics, we often study a sample to make inferences about a larger population. Choosing a suitable sampling method is crucial to avoid bias.
在统计学中，我们经常通过研究样本来推断更大规模的总体。选择合适的抽样方法对于避免偏差至关重要。
Population: the entire group of individuals or items that you want to investigate. The size of the population is often large.
总体：你想要调查的全部个体或项目组成的群体。总体规模通常很大。
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