📚 Year 11 Eduqas Statistics: Vocabulary & Terminology Quick Memorisation Guide | Year 11 Eduqas 统计：词汇术语速记指南
This guide is designed to help Year 11 Eduqas Statistics students master the essential terminology quickly and effectively. Each section pairs English explanations with Chinese translations, so you can understand every term in depth and commit it to memory. Use the memory tips and structured repetition to build confidence before your exams.
本指南旨在帮助 Year 11 Eduqas 统计学生快速有效地掌握核心术语。每个小节都以英文和中文配对讲解，让你深入理解每个术语并牢牢记住。利用记忆技巧和结构化复述，在考前建立信心。
1. Types of Data | 数据类型
Data is the raw information we collect and analyse. Understanding its type determines which statistical methods are appropriate. Data can be categorised as qualitative (describing qualities) or quantitative (measuring quantities), and quantitative data further splits into discrete and continuous.
数据是我们收集和分析的原始信息。了解其类型决定了适用的统计方法。数据可分为定性（描述性质）和定量（测量数量），定量数据又分为离散型和连续型。
Qualitative data consists of non-numerical descriptions like eye colour, gender or survey responses such as ‘yes/no’. It is often summarised using frequency counts and bar charts.
定性数据由非数值的描述组成，如眼睛颜色、性别或“是/否”调查答案。通常用频数统计和条形图来汇总。
Quantitative discrete data can only take specific numerical values, usually counts. For example, the number of students in a class or shoe size. There are gaps between possible values.
定量离散数据只能取特定的数值，通常是计数，比如班级学生人数或鞋码。可能取值之间存在间隔。
Quantitative continuous data can take any value within a range, such as height, weight or time. Measurements are limited only by the precision of the instrument, and histograms with frequency density are often used to display the data.
定量连续数据可以取某个范围内的任意值，如身高、体重或时间。测量值仅受仪器精度的限制，通常用带频率密度的直方图来展示。
Primary data is collected by the researcher first-hand through experiments or surveys. Secondary data is obtained from existing sources such as government statistics or published research.
一手数据由研究者通过实验或调查亲自收集。二手数据来自现有来源，如政府统计数据或已发表的研究。
2. Measures of Central Tendency | 集中量数
A measure of central tendency gives a typical or representative value for a data set. The three most common are the mean, median and mode. Each has strengths and weaknesses depending on the distribution of data.
集中量数给出数据集的典型值或代表值。最常见的三种是平均数、中位数和众数。根据数据分布的不同，各有优缺点。
The mean is the arithmetic average, calculated by adding all data values and dividing by the number of values. It uses every piece of data but can be heavily influenced by outliers.
平均数（均值）是算术平均值，通过将所有数据值相加再除以数据个数来计算。它利用了每个数据点，但容易受极端值的影响。
The median is the middle value when the data is arranged in ascending order. For an even number of data points, the median is the mean of the two central values. It is unaffected by outliers, making it the preferred measure for skewed distributions.
中位数是将数据按升序排列后的中间值。如果数据个数为偶数，中位数是中间两个数值的平均数。它不受极端值影响，因此是偏态分布中首选的集中量。
The mode is the most frequently occurring value. A data set can have one mode (unimodal), two modes (bimodal) or more. The mode is the only measure suitable for qualitative data.
众数是出现次数最多的值。一个数据集可能有一个众数（单峰）、两个众数（双峰）或更多。众数是唯一适用于定性数据的集中量。
Memory tip: Mean is the average affected by extremes, Median is the middle unaffected, Mode is the most frequent value. Use ‘MMM’ to recall them.
记忆窍门：Mean 是受极端值影响的平均值，Median 是不受影响的中位数，Mode 是出现最多的值。用“三 M”来记忆。
3. Measures of Spread | 离散量数
Measures of spread describe how spread out or consistent the data is. They complement measures of central tendency by showing variability. Key measures include range, interquartile range, variance and standard deviation.
离散量数描述数据的分散程度或一致性，补充集中量数以显示变异性。主要度量包括极差、四分位距、方差和标准差。
The range is the simplest measure, found by subtracting the smallest value from the largest value. It is easy to calculate but ignores most of the data and is sensitive to outliers.
极差是最简单的度量，由最大值减去最小值得到。它计算简单，但忽略了大部分数据，且对极端值敏感。
The interquartile range (IQR) is the difference between the upper quartile (Q₃) and the lower quartile (Q₁). It represents the spread of the middle 50% of the data and is robust against outliers.
四分位距（IQR）是上四分位数（Q₃）与下四分位数（Q₁）的差值，代表中间50%数据的分散程度，对异常值具有稳健性。
Quartiles divide ordered data into four equal parts. The lower quartile Q₁ is the median of the lower half of the data, and the upper quartile Q₃ is the median of the upper half. When finding quartiles, always order the data first.
四分位数将有序数据分成四等份。下四分位数 Q₁ 是数据下半部分的中位数，上四分位数 Q₃ 是上半部分的中位数。寻找四分位数时，务必先排序数据。
Variance measures the average squared deviation from the mean. The standard deviation is the square root of the variance. The formula for variance of a sample uses n-1 as the divisor: s² = ∑(x − x̄)² / (n − 1). Standard deviation is the most widely used measure of spread because it is in the same units as the original data.
方差衡量各数据与平均数之差的平方的平均值。标准差是方差的平方根。样本方差的公式使用 n−1 作为分母：s² = ∑(x − x̄)² ÷ (n − 1)。标准差是最常用的离散量数，因为其单位与原始数据相同。
Memory aid: Range = max − min, IQR = Q₃ − Q₁, and the standard deviation shows us how much data typically varies from the mean.
记忆辅助：极差 = 最大 − 最小，IQR = Q₃ − Q₁，标准差告诉我们数据通常与平均数偏离多少。
4. Presenting Data: Charts and Diagrams | 数据呈现：图表
Different types of data require different visual representations. Bar charts, pie charts, histograms, cumulative frequency graphs and box plots are essential for Eduqas Statistics. Choosing the correct diagram is part of the examination.
不同类型的数据需要不同的视觉呈现方式。条形图、饼图、直方图、累积频率图和箱线图是Eduqas统计的必考图表，选择合适的图表也是考试的一部分。
A bar chart is used for qualitative or discrete data. The bars are separate and of equal width; the height represents frequency. The categories can be arranged in any order.
条形图用于定性或离散数据。条形相互分离且宽度相等，高度表示频数。类别可以任意排列。
A histogram is used for continuous data. The area of each bar is proportional to the frequency, and there are no gaps between bars. Because class intervals may be unequal, we use frequency density = frequency ÷ class width.
直方图用于连续数据。每个条形的面积与频数成正比，条形之间没有间隙。由于组距可能不等，我们需要使用频率密度 = 频数 ÷ 组距。
A cumulative frequency graph plots the running total of frequencies against the upper class boundaries. It is used to estimate the median, quartiles and percentiles. Drawing a smooth curve through the points gives a cumulative frequency curve (ogive).
累积频率图将频数的累计总和相对于上组界绘制。它用于估计中位数、四分位数和百分位数。穿过各点画一条平滑曲线就得到了累积频率曲线。
A box plot (box-and-whisker plot) displays the five-number summary: minimum, Q₁, median, Q₃ and maximum. It clearly shows the centre, spread and any outliers. Outliers are often defined as values outside the fences Q₁ − 1.5×IQR and Q₃ + 1.5×IQR.
箱线图（箱须图）显示五数概括：最小值、Q₁、中位数、Q₃ 和最大值。它能清晰展示中心、分散程度和异常值。异常值通常定义为超出上下内限 Q₁ − 1.5×IQR 和 Q₃ + 1.5×IQR 的值。
A scatter diagram is used to show the relationship between two quantitative variables. The pattern can indicate positive, negative or no correlation. A line of best fit may be added to help make predictions.
散点图用来展示两个定量变量之间的关系。图形形态可显示正相关、负相关或无相关。可添加最佳拟合线以帮助预测。
5. Probability Terminology | 概率术语
Probability describes how likely an event is to happen, expressed as a number between 0 and 1. Clear definitions of events, sample space and probability rules are crucial for solving problems correctly.
概率描述某事件发生的可能性，用0到1之间的数字表示。清晰定义事件、样本空间和概率规则是正确解题的关键。
The sample space is the set of all possible outcomes of an experiment. An event is a subset of the sample space. For equally likely outcomes, probability = number of favourable outcomes ÷ total number of outcomes.
样本空间是实验所有可能结果的集合。事件是样本空间的一个子集。对于等可能结果，概率 = 有利结果的数量 ÷ 总结果的数量。
Mutually exclusive events cannot happen at the same time. The probability of A or B occurring is P(A ∪ B) = P(A) + P(B). This is the addition rule for mutually exclusive events.
互斥事件不能同时发生。A 或 B 发生的概率为 P(A ∪ B) = P(A) + P(B)。这是互斥事件的加法规则。
Independent events are those where the occurrence of one does not affect the probability of the other. The probability of both occurring is P(A ∩ B) = P(A) × P(B). The multiplication rule applies to independent events.
独立事件是指一个事件的发生不影响另一个事件发生概率的事件。两者同时发生的概率为 P(A ∩ B) = P(A) × P(B)。乘法规则适用于独立事件。
Conditional probability is the probability of an event given that another event has already occurred, written as P(A|B). The formula is P(A|B) = P(A ∩ B) / P(B), where P(B) > 0. Tree diagrams often help with multi-stage experiments.
条件概率是指在另一个事件已发生的条件下某事件发生的概率，记作 P(A|B)。公式为 P(A|B) = P(A ∩ B) / P(B)，其中 P(B) > 0。树状图通常有助于处理多阶段实验。
The complement of an event A, denoted A’, represents ‘not A’. The sum of the probabilities of an event and its complement is 1: P(A) + P(A’) = 1.
事件 A 的补集，记作 A’，表示“非 A”。事件和其补集的概率之和为 1：P(A) + P(A’) = 1。
6. Sampling Techniques | 抽样技术
A sample is a subset of a population used to make inferences about the whole group. The sampling method must be carefully chosen to avoid bias and ensure representativeness. Key terms include population, sample frame, and sample size.
样本是从总体中选出的子集，用于对整体进行推断。抽样方法必须谨慎选择以避免偏差并确保代表性。核心术语包括总体、抽样框和样本量。
In a simple random sample every member of the population has an equal chance of being selected. This can be done using random number generators or drawing lots. It is the fairest method but requires a complete list of the population, known as the sampling frame.
在简单随机抽样中，总体的每个成员被选中的机会均等。可以使用随机数生成器或抽签实现。这是最公平的方法，但需要一个完整的总体名单，即抽样框。
Stratified sampling divides the population into distinct groups (strata) and then takes a random sample from each group in proportion to its size. This ensures that each subgroup is fairly represented and reduces sampling error.
分层抽样将总体分为不同的组（层），然后按比例从每组中随机抽取样本。这确保了每个子群被公平代表，并减少了抽样误差。
Systematic sampling selects members at regular intervals from an ordered list, e.g. every 10th person. It is easy to implement but can lead to bias if there is a hidden pattern in the list.
系统抽样从有序名单中每隔固定间隔选取成员，例如每10人选1人。它易于实施，但如果名单中存在隐藏模式，可能导致偏差。
Bias occurs when a sample is not representative of the population. Common types include selection bias, non-response bias and measurement bias. A well-designed sampling strategy aims to minimise bias.
偏差发生在样本不能代表总体时。常见类型包括选择偏差、无回应偏差和测量偏差。设计良好的抽样策略旨在将偏差降至最低。
A convenience sample uses readily available participants, like friends or people nearby. It is quick and cheap but usually produces highly biased results and should be avoided in serious statistical work.
便利抽样使用容易获得的参与者，如朋友或附近的人。它快速且成本低，但通常会产生高度偏差的结果，在严肃的统计工作中应避免使用。
7. Correlation and Regression | 相关与回归
Correlation describes the strength and direction of a linear relationship between two variables. Regression goes further by modelling the relationship with an equation that can be used for prediction.
相关描述两个变量之间线性关系的强度和方向。回归则更进一步，用方程式对关系进行建模，用以预测。
Positive correlation means that as one variable increases, the other also tends to increase. Negative correlation means that as one increases, the other tends to decrease. If there is no apparent pattern, we say there is zero or no correlation.
正相关意味着一个变量增加时，另一个也趋于增加。负相关意味着一个增加时另一个趋于减少。如果没有明显模式，我们称其为零相关或无相关。
The correlation coefficient r measures the strength of a linear relationship. Its value lies between −1 and +1. Values close to +1 indicate strong positive correlation, values close to −1 indicate strong negative correlation, and values near 0 indicate weak or no linear correlation. There is no need to calculate r in Year 11 Eduqas, but you must interpret given values.
相关系数 r 衡量线性关系的强度。其值介于 −1 和 +1 之间。接近 +1 表示强正相关，接近 −1 表示强负相关，接近 0 表示弱线性相关或无线性相关。Eduqas Year 11 无需计算 r，但必须能解释给定的数值。
The regression line is a straight line of best fit on a scatter diagram. The equation of the line is often written as y = a + bx, where a is the intercept and b is the gradient. In the context of statistics, regression lines are used to predict values of the response variable for given values of the explanatory variable.
回归线是散点图上的最佳拟合直线。方程通常写作 y = a + bx，其中 a 是截距，b 是斜率。在统计情境中，回归线用于根据给定的解释变量值预测响应变量的值。
Interpolation is the estimation of a value within the range of the data, which is generally reliable. Extrapolation is the estimation outside the range of the data and can be unreliable because the trend may not continue.
内插法是在数据范围内进行估值，通常可靠。外推法是在数据范围之外进行估值，由于趋势可能不会延续，因此可能不可靠。
8. Statistical Notation and Symbols | 统计符号速记
Recognising and using statistical symbols correctly is essential for understanding questions and writing answers clearly. The following symbols are used throughout the Eduqas specification.
正确识别和使用统计符号对于理解题目和清晰作答至关重要。以下符号贯穿 Eduqas 考试大纲。
The symbol Σ (Greek capital sigma) means ‘sum of’. For example, Σx means the sum of all data values. Σf means the sum of frequencies, which gives the total number of observations.
符号 Σ（希腊大写字母西格玛）表示“求和”。例如，Σx 表示所有数据值的总和。Σf 表示频数之和，即观察总数。
The symbol x̄ (x-bar) represents the sample mean, while μ (mu) is used for the population mean. In GCSE Statistics, x̄ is the standard notation for the mean of a sample or a set of data.
符号 x̄（x 拔）代表样本平均数，而 μ（缪）用于总体平均数。在 GCSE 统计中，x̄ 是表示样本或一组数据均值的标准符号。
For variance and standard deviation, s² and s are used for a sample, while σ² and σ (sigma) denote population parameters. The five-number summary is often represented as: Min, Q₁, Med (or Q₂), Q₃, Max.
对于方差和标准差，样本用 s² 和 s，而 σ² 和 σ 表示总体参数。五数概括常表示为：Min, Q₁, Med（或 Q₂）, Q₃, Max。
The symbol n usually stands for sample size, and N for population size. The notation for a complementary event is A’ or sometimes Aᶜ. The intersection of two events is written as A ∩ B, and the union as A ∪ B.
符号 n 通常表示样本量，N 表示总体规模。互补事件的记号为 A’ 或有时 Aᶜ。两个事件的交集写作 A ∩ B，并集写作 A ∪ B。
Probability is denoted by P. For example, P(A) is the probability of event A, and P(A|B) is the conditional probability of A given B. Familiarity with these symbols will speed up your reading of questions.
概率用 P 表示。例如，P(A) 是事件 A 的概率，P(A|B) 是在 B 发生的条件下 A 的条件概率。熟悉这些符号能加快你阅读题目的速度。
9. Summary of Key Formulas | 核心公式汇总
Memorising the main formulas will help you apply them quickly in the exam. Here are the most important ones, presented with correct notation. All calculations can be done with a calculator, but understanding the structure is vital.
记住主要公式能帮助你在考试中快速应用。以下是最重要的公式，配以正确的符号。所有计算都可用计算器完成，但理解结构至关重要。
Mean (ungrouped): x̄ = Σx / n
平均数（未分组）：x̄ = Σx / n
Mean (grouped): x̄ = Σfx / Σf
平均数（分组）：x̄ = Σfx / Σf
Range = Max − Min
极差 = 最大值 − 最小值
Interquartile Range = Q₃ − Q₁
四分位距 = Q₃ − Q₁
Variance (sample): s² = Σ(x − x̄)² / (n − 1)
方差（样本）：s² = Σ(x − x̄)² / (n − 1)
Standard deviation (sample): s = √[ Σ(x − x̄)² / (n − 1) ]
标准差（样本）：s = √[ Σ(x − x̄)² / (n − 1) ]
Frequency density = frequency / class width
频率密度 = 频数 / 组距
Probability of an event: P(A) = number of ways A can occur / total number of outcomes
事件概率：P(A) = A 可发生的方式数 / 总结果数
For grouped data, use the midpoints of class intervals as x. Always check whether the data represents a sample or a population before deciding whether to divide by n or n−1.
对于分组数据，使用组距的中点作为 x。在决定除以 n 还是 n−1 之前，务必检查数据代表的是样本还是总体。
10. Common Errors and Exam Tips | 常见错误与考试技巧
Avoiding common mistakes can significantly improve your score. This section highlights typical errors and provides practical tips for the Eduqas Statistics paper.
避免常见错误能显著提高你的分数。本节重点指出常见错误，并为 Eduqas 统计试卷提供实用技巧。
Many students confuse discrete and continuous data when choosing a diagram. Always ask: ‘Can this data take any value in between or only certain values?’ Use bar charts for discrete data and histograms for continuous data.
许多学生在选择图表时会混淆离散和连续数据。一定要问自己：“这个数据能取中间的任何数值吗，还是只能取某些值？”离散数据用条形图，连续数据用直方图。
When calculating the mean from a frequency table, remember to multiply each value by its frequency, sum these products and then divide by the total frequency. Forgetting to multiply is a frequent slip.
当根据频数表计算平均数时，记得用每个值乘以它的频数，将这些乘积相加，然后除以总频数。忘记乘这一步骤是常见失误。
For IQR, always find Q₁ and Q₃ correctly after ordering the data. A mistake is taking the median of the whole list and then incorrectly splitting the halves. Ensure you exclude the median itself when the list size is odd, following the exam board’s preferred method.
对于 IQR，务必在数据排序后正确找到 Q₁ 和 Q₃。一个常见错误是先求整个列表的中位数，然后错误地分割数据。当列表大小为奇数时，根据考试局推荐的方法，要确保排除中位数本身。
When interpreting correlation, do not assume causation. A strong correlation does not prove that one variable causes the other to change; there could be a third factor involved.
在解释相关性时，不要假定因果关系。强相关并不能证明一个变量导致另一个变化；可能有第三个因素参与其中。
In probability questions, check whether events are mutually exclusive or independent before applying addition or multiplication rules. Drawing a Venn diagram or tree diagram can prevent logic errors.
在概率题中，先检查事件是互斥还是独立，再应用加法或乘法规则。画文氏图或树状图可以防止逻辑错误。
Always include units in your final answers when quantities have units. Also, write a short commentary if asked to compare data sets; mention both a measure of central tendency and a measure of spread to fully support your comparison.
当数量有单位时，最终答案中务必包含单位。此外，如果要求比较数据集，请写一个简短的评论；同时提及集中量数和离散量数，以充分支持你的比较。
Finally, show all working out step by step, even if you use a calculator. Method marks are awarded for correct processes, and clear working can earn you marks even if the final answer is wrong.
最后，即使使用计算器，也要逐步展示所有计算过程。过程分会给正确的步骤，清晰的解题过程即使最终答案错误也能让你得分。
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