📚 Year 10 SQA Statistics: Vocabulary & Terminology Quick Memorisation Guide | 10年级 SQA 统计：词汇术语速记指南
Building a solid foundation in statistics begins with understanding the language of data. This guide takes you through the key terms, symbols and definitions you will meet in the Year 10 SQA Statistics course. Each term is presented with a clear English explanation followed by its Chinese equivalent, along with helpful memory tips to make revision faster and more effective.
在统计学中打下坚实基础，首先要理解数据的语言。本指南将带你梳理 10 年级 SQA 统计课程中会遇到的关键术语、符号和定义。每个术语先给出清晰的英文解释，再给出对应的中文释义，并附上实用的记忆技巧，让复习更高效、更轻松。
1. Basic Statistical Terms | 基础统计术语
Statistics is the science of collecting, organising, analysing and interpreting data. Before diving into calculations, you need to know the building blocks: population, sample, variable and parameter.
统计学是收集、整理、分析和解释数据的科学。在深入计算之前，你需要了解一些基本构件：总体、样本、变量和参数。
Population – the complete set of items or individuals that we want to investigate. For example, all S4 pupils in Scotland.
总体 – 我们想要研究的全部项目或个体的集合。例如，苏格兰所有 S4 年级的学生。
Sample – a subset of the population selected to represent it. Studying a sample saves time and money.
样本 – 从总体中选出的、具有代表性的子集。研究样本可以节省时间和成本。
Variable – any characteristic or quantity that can take different values, such as height, test score or eye colour.
变量 – 可以取不同值的特征或数量，如身高、测验分数或眼睛颜色。
Parameter – a numerical summary that describes a characteristic of a population, for example the population mean (μ).
参数 – 描述总体某一特征的数值概括，例如总体均值 (μ)。
Statistic – a numerical summary calculated from a sample, used to estimate a population parameter, such as the sample mean (x̄).
统计量 – 从样本中计算出来的数值概括，用于估计总体参数，例如样本均值 (x̄)。
Observation – a single recorded measurement or data point. Each row in a spreadsheet often represents one observation.
观测值 – 单个记录的测量值或数据点。电子表格中的每一行通常代表一个观测值。
2. Measures of Central Tendency | 集中趋势的度量
A measure of central tendency identifies the centre or typical value of a data set. The three most common averages are the mean, median and mode.
集中趋势的度量用于确定数据集的中心或典型值。最常用的三种平均数是均值、中位数和众数。
Mean – the arithmetic average, found by summing all values and dividing by the number of values. Think of it as sharing equally; the word 'mean' sounds like 'even' which can remind you of an even distribution.
均值 – 算术平均数，通过将所有数值相加再除以数值个数得到。可以想象成平均分配；'mean' 听起来像 'even'，提醒你它是均匀分配的。
Mean = ∑x / n
Median – the middle value when data are arranged in order. If there are two middle numbers, take their mean. Memory hook: 'median' contains 'mid', like the central strip of a motorway.
中位数 – 将数据按顺序排列后处于中间位置的值。如果有两个中间数，则取它们的均值。记忆窍门：'median' 里藏着 'mid'，就像高速公路的中央隔离带。
Mode – the value that occurs most frequently. A data set can have one mode, more than one mode (bimodal or multimodal) or no mode at all. The word 'mode' sounds like 'most' – the most popular option.
众数 – 出现频率最高的值。数据集可以有一个众数、多个众数（双众数或多众数）或没有众数。'mode' 听起来像 'most'——最常见的选项。
Weighted mean – an average where some values contribute more weight than others. Useful when combining marks from assessments with different percentages.
加权均值 – 每个数值对平均值的贡献权重不同的平均数。当需要合并不同占比的评估分数时很有用。
3. Measures of Dispersion | 离散程度的度量
Dispersion tells us how spread out the data are around the centre. A small spread means the data are tightly clustered; a large spread indicates high variability.
离散程度告诉我们数据围绕中心的分散情况。离散程度小意味着数据紧密聚集；离散程度大则表明变异性高。
Range – the difference between the maximum and minimum values. Easy to calculate but highly affected by outliers.
极差 – 最大值与最小值之差。计算简单，但极易受异常值影响。
Quartiles – values that divide an ordered data set into four equal parts: Q₁ (lower quartile), Q₂ (median) and Q₃ (upper quartile). Remember 'Q' for 'quarters'.
四分位数 – 将有序数据集分成四等份的值：Q₁ (下四分位数)、Q₂ (中位数) 和 Q₃ (上四分位数)。'Q' 让你联想到 'quarters'（四分之一）。
Interquartile range (IQR) – the range of the middle 50% of the data, calculated as Q₃ – Q₁. IQR is resistant to outliers, making it a robust measure of spread.
四分位距 (IQR) – 中间 50% 数据的跨度，计算公式为 Q₃ – Q₁。IQR 不受异常值影响，是稳健的离散度量。
IQR = Q₃ – Q₁
Variance (s²) – the average of the squared differences from the mean. It shows how much the data deviate from the centre in squared units.
方差 (s²) – 各数据与均值之差的平方的平均数。它用平方单位表示数据偏离中心的程度。
Standard deviation (s) – the square root of the variance, returning to the original units. The larger the standard deviation, the more spread out the data.
标准差 (s) – 方差的平方根，恢复到原始单位。标准差越大，数据越分散。
4. Types of Data | 数据类型
Recognising the type of data you are working with helps you choose the right graph and summary statistic. Data can be broadly split into qualitative and quantitative.
认清你所处理的数据类型有助于选择合适的图表和汇总统计量。数据可大致分为定性数据和定量数据。
Qualitative (categorical) data – non-numerical information that describes qualities or categories, such as hair colour, favourite subject or postcode. Do not try to find a mean – use mode or bar charts.
定性（分类）数据 – 描述性质或类别的非数值信息，如头发颜色、最喜欢的科目或邮政编码。不要试图计算均值——使用众数或条形图。
Quantitative data – numerical data that can be measured or counted. Quantitative data divides further into discrete and continuous types.
定量数据 – 可以测量或计数的数值数据。定量数据进一步分为离散型和连续型。
Discrete data – can only take specific, separate values (often whole numbers). Examples: number of siblings, shoe size, goals scored. You cannot have 2.3 siblings.
离散数据 – 只能取特定、分离的值（通常是整数）。例如：兄弟姐妹人数、鞋码、进球数。你不可能有 2.3 个兄弟姐妹。
Continuous data – can take any value within a range, including decimals. Examples: height, weight, time, temperature. Measurements fall into this category.
连续数据 – 在某个范围内可以取任意值，包括小数。例如：身高、体重、时间、温度。测量值属于这类数据。
Nominal and ordinal scales – nominal data name categories without order (e.g. eye colour); ordinal data have a meaningful order but unequal intervals (e.g. satisfaction rating). Remember 'ordinal' sounds like 'order'.
名义尺度与顺序尺度 – 名义数据只是给类别命名，没有顺序（如眼睛颜色）；顺序数据则有有意义的顺序，但间隔不一定相等（如满意度评分）。记住 'ordinal' 听起来像 'order'。
5. Sampling Techniques | 抽样技术
Because we rarely have access to a whole population, we use samples. The way we select a sample matters – a poor method leads to bias and unreliable conclusions.
由于我们很少能获取整个总体，因此需要使用样本。选择样本的方式至关重要——方法不当会导致偏差和不可靠的结论。
Simple random sampling – every member of the population has an equal chance of being selected. Think of drawing names from a hat or using a random number generator.
简单随机抽样 – 总体中每个成员被选中的机会均等。可以想象成从帽子里抽名字或使用随机数生成器。
Stratified sampling – the population is divided into groups (strata) that share a common characteristic, then a random sample is taken from each group in proportion to its size. The word 'strata' suggests layers – like layers in a cake.
分层抽样 – 将总体按共同特征分成若干组（层），然后从每组中按比例随机抽取样本。'strata' 暗示层次——像蛋糕的分层。
Systematic sampling – selecting every k-th individual from a list after a random start. For example, surveying every 10th customer. It is systematic because a fixed pattern is used.
系统抽样 – 随机确定起点后，在列表中每隔 k 个个体选取一个。例如，每第 10 位顾客调查一次。它之所以系统，是因为使用了固定的模式。
Cluster sampling – the population is split into clusters (often geographically), and entire clusters are randomly selected. Useful when a complete list of the population is unavailable.
整群抽样 – 将总体分成若干群（通常按地理划分），然后随机选取整群。当无法获得完整的总体名单时很有用。
Convenience sampling – choosing individuals who are easiest to reach, such as friends or the first people you see. This method often introduces serious bias.
便利抽样 – 选择最容易接触到的人，比如朋友或最先遇到的人。这种抽样常会带来严重偏差。
Bias – a systematic error that causes a sample to misrepresent the population. Biased samples lead to invalid conclusions. Think of 'bias' as leaning unfairly in one direction.
偏差 – 导致样本无法代表总体的系统性误差。有偏差的样本会得出无效的结论。可将 'bias' 理解为不公平地向某一方向倾斜。
6. Probability Fundamentals | 概率基础
Probability is the branch of mathematics that deals with chance and uncertainty. It gives us a numerical way to describe how likely an event is to happen.
概率是研究机会和不确定性的数学分支。它为我们提供了一种用数值描述某事件发生可能性的方法。
Experiment – any process that produces an outcome, such as rolling a die or measuring rainfall.
试验 – 产生结果的任何过程，如掷骰子或测量降雨量。
Outcome – a possible result of an experiment. When tossing a coin, heads and tails are the two possible outcomes.
结果 – 试验可能产生的某个结果。抛硬币时，正面和反面是两个可能的结果。
Sample space – the set of all possible outcomes, usually denoted by S. For a die, S = {1, 2, 3, 4, 5, 6}.
样本空间 – 所有可能结果的集合，通常用 S 表示。对于一枚骰子，S = {1, 2, 3, 4, 5, 6}。
Event – ubset of the sample space. For example, rolling an even number is the event E = {2, 4, 6}.
事件 – 样本空间的一个子集。例如，掷出偶数是事件 E = {2, 4, 6}。
Probability of an event – a number between 0 and 1 that measures the chance that the event occurs. Calculated as (number of favourable outcomes) / (total number of outcomes) when all outcomes are equally likely.
事件概率 – 介于 0 和 1 之间的一个数，用来衡量该事件发生的可能性。当所有结果等可能时，用（有利结果数）/（总结果数）计算。
Independent events – two events where the occurrence of one does not affect the probability of the other. Rolling a die twice yields independent outcomes.
独立事件 – 一个事件的发生不影响另一个事件发生的概率。掷两次骰子，两次结果是独立的。
Mutually exclusive events – events that cannot happen at the same time, such as getting heads and tails on a single coin toss. Their probabilities add up without subtraction.
互斥事件 – 不可能同时发生的事件，如抛一次硬币同时得到正面和反面。它们的概率可以直接相加而不需要相减。
Relative frequency – le, if it rained on 12 of the last 30 days, the relative frequency of rain is 12/30 = 0.4.
相对频率 – 基于重复试验或历史数据对概率的估计。例如，如果过去 30 天中有 12 天下雨，则下雨的相对频率为 12/30 = 0.4。
7. Correlation and Causation | 相关与因果
When we have two variables, we often want to explore whether they are related. Correlation measures this relationship, but it does not automatically mean one variable causes the other.
当我们有两个变量时，常常想探究它们之间是否存在关系。相关性衡量这种关系，但它并不自动意味着一个变量导致了另一个。
Scatter diagram (scatter plot) – a graph that displays pairs of values for two numerical variables. Each point represents one observation. Patterns in the points suggest correlation.
散点图 – 展示两个数值变量配对的图表。每个点代表一个观测值。点的分布形态暗示着相关关系。
Positive correlation – as one variable increases, the other also tends to increase. The points slope upwards. Example: height and weight generally show a positive correlation.
正相关 – 一个变量增加，另一个也趋向增加。点呈向上倾斜的形态。例如：身高和体重通常呈正相关。
Negative correlation – as one variable increases, the other tends to decrease. The points slope downwards. Example: the more hours a student watches TV, the lower their test score might be.
负相关 – 一个变量增加，另一个趋向减少。点呈向下倾斜的形态。例如：学生看电视时间越长，测验分数可能越低。
No correlation – the points show no clear upward or downward pattern; the variables appear unrelated.
无相关 – 点的分布没有明显的上升或下降形态；变量似乎不相关。
Correlation coefficient (r) – a number between -1 and +1 that measures the strength and direction of a linear relationship. 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.
相关系数 (r) – 介于 -1 和 +1 之间的数，用于衡量线性关系的强度和方向。接近 +1 表示强正相关，接近 -1 表示强负相关，接近 0 表示线性相关弱或无相关。
Line of best fit – a straight line drawn through the centre of the points on a scatter plot to model the relationship. It can be used to make predictions within the range of the data (interpolation).
最佳拟合线 – 穿过散点图中点群中心的一条直线，用于建模变量间的关系。可用于在数据范围内进行预测（内插）。
Causation – when a change in one variable directly produces a change in another. Remember: correlation does not imply causation. A third hidden factor (confounding variable) might be responsible for the association.
因果关系 – 一个变量的改变直接导致另一个变量改变。记住：相关不代表因果。可能有第三个隐藏因素（混杂变量）造成了两者间的关联。
8. Charts and Diagrams | 统计图表
Different types of data require different visual representations. Choosing the right diagram makes patterns easy to spot and comparisons clear.
不同类型的数据需要不同的可视化呈现。选择正确的图表能让规律易于发现、比较一目了然。
Bar chart – uses rectangular bars to represent frequencies of categorical data. The bars do not touch
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