📚 Year 10 SQA Statistics: Quick Vocabulary & Terminology Guide | Year 10 SQA 统计：词汇术语速记指南
Mastering statistical vocabulary is essential for success in SQA Statistics in Year 10. This guide provides clear definitions and mnemonic tips to help you remember key terms efficiently.
掌握统计词汇对于 Year 10 SQA 统计学的成功至关重要。本指南提供清晰的定义和记忆技巧，帮助你高效记住关键术语。
1. Measures of Central Tendency (Mean, Median, Mode) | 集中趋势度量 (均值、中位数、众数)
Mean: The arithmetic average, calculated as the sum of all data values divided by the number of values. Symbolically, x̄ = Σxᵢ / n.
均值：算术平均数，计算为所有数据值之和除以数值个数。符号表示为 x̄ = Σxᵢ / n。
Median: The middle value when data are arranged in order. For an even number of data points, the median is the average of the two middle numbers.
中位数：按顺序排列后处于中间位置的值。如果数据个数为偶数，中位数是中间两个数的平均值。
Mode: The value that occurs most frequently. A data set may have one mode (unimodal), two modes (bimodal), or more (multimodal).
众数：出现频率最高的值。数据集可能有一个众数（单峰）、两个众数（双峰）或多个众数（多峰）。
2. Measures of Dispersion (Range, IQR, Variance, Standard Deviation) | 离散程度度量 (极差、四分位距、方差、标准差)
Range: The difference between the highest and lowest values. It is a simple measure of spread but easily affected by outliers.
极差 (Range)：最大值与最小值的差值。它是一种简单的离散度量，但容易受异常值影响。
Interquartile Range (IQR): The difference between the upper quartile (Q3) and lower quartile (Q1). IQR = Q3 − Q1. It measures the spread of the middle 50% of the data and is resistant to outliers.
四分位距 (IQR)：上四分位数 (Q3) 与下四分位数 (Q1) 的差。IQR = Q3 − Q1。它衡量中间50%数据的离散程度，对异常值不敏感。
Variance: The average of the squared differences from the mean. For a sample, s² = Σ(xᵢ − x̄)² / (n − 1). It is in squared units.
方差：各数据与均值之差的平方的平均数。样本方差公式 s² = Σ(xᵢ − x̄)² / (n − 1)。单位是原单位的平方。
Standard Deviation: The square root of the variance. s = √[Σ(xᵢ − x̄)² / (n − 1)]. It is in the original units and commonly used to measure spread.
标准差：方差的平方根。公式 s = √[Σ(xᵢ − x̄)² / (n − 1)]。单位与原数据相同，常用于衡量离散程度。
3. Quartiles and Five-Number Summary | 四分位数与五数概括
Quartiles: Values that divide an ordered data set into four equal parts. Q1 (lower quartile) is the median of the lower half; Q3 (upper quartile) is the median of the upper half. Q2 is the median.
四分位数：将有序数据集分成四等份的值。Q1（下四分位数）是下半部分的中位数；Q3（上四分位数）是上半部分的中位数。Q2 就是中位数。
Five-Number Summary: Consists of minimum, Q1, median (Q2), Q3, and maximum. It provides a concise overview of the distribution and is used to create box plots.
五数概括：由最小值、Q1、中位数(Q2)、Q3、最大值组成。它提供了数据分布的简洁概述，并用于绘制箱线图。
4. Probability Fundamentals (Sample Space, Events) | 概率基础 (样本空间、事件)
Probability: A measure of the likelihood that an event will occur, ranging from 0 (impossible) to 1 (certain). P(event) = number of favourable outcomes / total number of outcomes.
概率：衡量事件发生可能性的指标，范围从0（不可能）到1（必然）。P(事件) = 有利结果数 / 总结果数。
Sample Space: The set of all possible outcomes of a probability experiment. Often denoted by S or Ω. E.g., tossing a coin: S = {Heads, Tails}.
样本空间：概率实验所有可能结果的集合。常用 S 或 Ω 表示。例如抛硬币：S = {正面, 反面}。
Event: A subset of the sample space. An event A can consist of one or more outcomes. P(A) is the probability that A occurs.
事件：样本空间的一个子集。事件 A 可以包含一个或多个结果。P(A) 是事件 A 发生的概率。
5. Types of Probability (Theoretical, Experimental, Relative Frequency) | 概率类型 (理论概率、实验概率、相对频率)
Theoretical Probability: Based on mathematical reasoning and known outcomes. P(rolling a 3 on a fair die) = 1/6.
理论概率：基于数学推理和已知可能结果。投掷一个公平骰子得到3的概率为1/6。
Experimental Probability (Relative Frequency): Based on actual trials or experiments. Relative frequency = number of times event occurs / total number of trials. As trials increase, it tends to approach theoretical probability.
实验概率 (相对频率)：基于实际试验或实验。相对频率 = 事件发生次数 / 总试验次数。随着试验次数增加，它会趋近于理论概率。
6. Mutually Exclusive and Independent Events | 互斥事件与独立事件
Mutually Exclusive Events: Two events that cannot occur at the same time. P(A and B) = 0. For mutually exclusive events A and B, P(A or B) = P(A) + P(B).
互斥事件：不能同时发生的两个事件。P(A 且 B) = 0。对于互斥事件 A 和 B，P(A 或 B) = P(A) + P(B)。
Independent Events: Events where the occurrence of one does not affect the probability of the other. P(A and B) = P(A) × P(B). E.g., tossing a coin twice.
独立事件：一个事件的发生不影响另一个事件概率的事件。P(A 且 B) = P(A) × P(B)。例如，两次抛硬币。
7. Conditional Probability | 条件概率
Conditional Probability: The probability of event A given that event B has occurred. Notation: P(A|B) = P(A and B) / P(B), provided P(B) > 0.
条件概率：在事件 B 已经发生的条件下事件 A 发生的概率。记法：P(A|B) = P(A 且 B) / P(B)，前提 P(B) > 0。
Tree Diagrams: Useful for visualising conditional probabilities and calculating combined probabilities by multiplying along branches.
树状图：用于可视化条件概率并通过沿线相乘计算联合概率。
8. Discrete vs. Continuous Data | 离散数据与连续数据
Discrete Data: Data that can only take specific, separate values, often integers. Examples: number of students, shoe size.
离散数据：只能取特定、分离值的数据，通常是整数。例如：学生人数、鞋码。
Continuous Data: Data that can take any value within a given range. Measurements like height, weight, time are continuous. It is often grouped into intervals.
连续数据：可以在给定范围内取任意值的数据。身高、体重、时间等测量值是连续的。通常被分组成区间。
9. Graphical Representations (Histogram, Frequency Polygon, Cumulative Frequency Curve) | 图形表示 (直方图、频率多边形、累积频率曲线)
Histogram: A graphical display of grouped continuous data. The area of each bar is proportional to the frequency, so frequency density (frequency ÷ class width) is used on the vertical axis.
直方图：分组连续数据的图形展示。每个条形的面积与频率成比例，因此纵轴使用频率密度（频率 ÷ 组距）。
Frequency Polygon: A line graph formed by joining the midpoints of the tops of histogram bars. Useful for comparing distributions.
频率多边形：通过连接直方图各条顶部中点形成的折线图。适用于比较分布。
Cumulative Frequency Curve (Ogive): A graph of cumulative frequency against the upper class boundary. It is used to estimate medians, quartiles, and percentiles.
累积频率曲线 (Ogive)：累积频率相对于组上限的图形。用于估计中位数、四分位数和百分位数。
10. Scatter Plots, Correlation, and Line of Best Fit | 散点图、相关性与最佳拟合线
Scatter Plot: A graph of paired bivariate data, with points representing (x, y) values. It reveals relationships between two variables.
散点图：成对二元数据的图表，点表示 (x, y) 值。它揭示两个变量之间的关系。
Correlation: Describes the strength and direction of a linear relationship. Positive correlation: as x increases, y tends to increase. Negative correlation: as x increases, y tends to decrease. No correlation if no pattern. Measured by correlation coefficient r.
相关：描述线性关系的强度和方向。正相关：x 增大，y 也倾向于增大。负相关：x 增大，y 倾向于减小。无相关则没有明显模式。由相关系数 r 度量。
Line of Best Fit: A straight line drawn through a scatter plot that best represents the trend. It can be used to make predictions (interpolation within data range, extrapolation outside).
最佳拟合线：穿过散点图的直线，最能代表趋势。可用于预测（数据范围内的内插，范围外的外推）。
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