📚 Year 9 AQA Statistics: Key Vocabulary Quick-Reference Guide | Year 9 AQA 统计：词汇术语速记指南
Mastering statistical terminology is the first step to success in your Year 9 AQA Statistics course. This quick-reference guide provides bilingual explanations of essential terms, grouped by topic, to help you build a solid foundation and recall key vocabulary quickly.
掌握统计术语是在 Year 9 AQA 统计课程中取得成功的第一步。本速记指南按主题分组提供重要术语的双语解释，帮助你打下坚实基础并快速记忆关键词汇。
1. Types of Data | 数据类型
Qualitative data describes qualities or characteristics, such as eye colour or favourite subject. It is often called categorical data and is usually non-numerical.
定性数据描述性质或特征，例如眼睛颜色或最喜欢的科目。它通常称为分类数据，一般是非数值的。
Quantitative data is numerical and can be measured or counted. It is further divided into discrete data (countable, e.g. number of students) and continuous data (measurable, e.g. height in cm).
定量数据是数值型数据，可以测量或计数。它进一步分为离散数据（可计数，如学生人数）和连续数据（可测量，如身高厘米数）。
A quick memory tip: 'Qualitative = Quality' (descriptive) and 'Quantitative = Quantity' (numbers). Discrete data often answers 'how many?' while continuous data answers 'how much?'
记忆技巧：‘定性’联想‘性质’，‘定量’联想‘数量’。离散数据回答‘多少个？’，连续数据回答‘多少？’
2. Data Collection Methods | 数据收集方法
Primary data is information you collect yourself for a specific purpose, such as conducting a survey or an experiment. It is up-to-date but can be time-consuming to gather.
一手数据是你自己为特定目的收集的信息，比如进行问卷调查或实验。它是最新数据，但收集起来可能很耗时。
Secondary data is data that has already been collected by someone else, like government statistics or internet sources. It is quicker to obtain but may be less reliable or not perfectly suited to your research question.
二手数据是别人已经收集好的数据，比如政府统计数据或网络资料。获取速度较快，但可能不够可靠或不完全切合你的研究问题。
A hypothesis is a clear statement predicting what you expect to find in your investigation. For example, 'Students who study more hours per week achieve higher test scores.'
假设是一个清晰的陈述，预测你在调查中期望发现的结果。例如：‘每周学习时间更多的学生考试成绩更高。’
A pilot survey is a small trial run of your questionnaire or data collection method, used to identify any problems before the full study.
试点调查是对问卷或数据收集方法进行的小规模试行，用于在全面研究前找出潜在问题。
3. Averages: Mean, Median & Mode | 平均数：均值、中位数和众数
The mean is the sum of all values divided by the number of values. It is often called the 'average' but can be affected by extreme values (outliers).
均值是所有数值的总和除以数值的个数。它常被称为‘平均数’，但容易受极端值（异常值）影响。
Mean = (sum of all data values) ÷ (number of data values)
均值 = (所有数据值之和) ÷ (数据个数)
The median is the middle value when the data is arranged in order. For an even number of values, it is the mean of the two middle numbers. The median is not affected by outliers, making it useful for skewed data.
中位数是将数据按顺序排列后的中间值。如果数据个数为偶数，则取中间两个数的平均值。中位数不受异常值影响，因此适用于偏斜数据。
The mode is the value that appears most often. A data set can have one mode (unimodal), two modes (bimodal) or no mode if all values occur only once.
众数是出现次数最多的数值。数据集可能有一个众数（单峰）、两个众数（双峰）或没有众数（如果所有值只出现一次）。
Tip: remember 'median' sounds like 'medium' – it's in the middle. 'Mode' starts with 'mo' like 'most'.
技巧：‘中位数’就是中间那个；‘众数’联想‘众’即最多。
4. Measures of Spread: Range, Quartiles & IQR | 离散程度：极差、四分位数及四分位距
The range is the difference between the largest and smallest values. It gives a simple measure of how spread out the data is.
极差是最大值与最小值之差。它反映了数据分散程度的简单度量。
Range = maximum value – minimum value
极差 = 最大值 – 最小值
The lower quartile (Q₁) is the median of the lower half of the data. The upper quartile (Q₃) is the median of the upper half. Together with the median (Q₂), they split the data into four equal parts.
下四分位数 (Q₁) 是数据下半部分的中位数。上四分位数 (Q₃) 是数据上半部分的中位数。与中位数 (Q₂) 一起，它们将数据分成四个等份。
The interquartile range (IQR) = Q₃ – Q₁. It measures the spread of the middle 50% of the data and is more resistant to outliers than the range.
四分位距 (IQR) = Q₃ – Q₁。它衡量中间 50% 数据的分散程度，比极差更能抵抗异常值的影响。
Quick memory: Q₁ = first quarter break, Q₃ = third quarter break. IQR focuses on the 'middle half'.
记忆技巧：Q₁ 是第一个四等分点，Q₃ 是第三个；IQR 关注‘中间一半’。
5. Charts & Diagrams Part 1: Bar Charts, Pie Charts, Pictograms | 图表与图示（一）：柱状图、饼图、象形图
Bar charts display categorical data with rectangular bars where the length or height represents frequency. The bars are separated to show distinct categories. A vertical bar chart is often called a column chart.
柱状图用柱形条展示分类数据，条的长度或高度表示频数。条与条之间有间隔，表明不同的类别。垂直的柱状图也常称为条形图。
Pie charts show proportions of a whole. Each sector' l) × 360°. They are useful for comparing parts of a whole but not for precise comparisons.
饼图展示整体中的比例关系。每个扇形的角度计算为 (频数 ÷ 总数) × 360°。适合比较部分与整体的关系，但不适于精确比较。
Pictograms use symbols or pictures to represent frequencies. A key tells you how many units each symbol represents. They are visually attractive but can be misleading if symbols are not drawn to scale.
象形图用符号或图片表示频数。图例会告诉你每个符号代表多少单位。它视觉上有吸引力，但如果符号不按比例绘制可能会产生误导。
When interpreting any chart, always read the title, axes labels and scales. A common exam mistake is forgetting to check the key on a pictogram.
解释任何图表时，一定要阅读标题、坐标轴标签和刻度。常见考试错误是忘记检查象形图的图例。
6. Charts & Diagrams Part 2: Stem-and-Leaf & Box Plots | 图表与图示（二）：茎叶图与箱线图
A stem-and-leaf diagram organises numerical data while retaining the original values. The 'stem' represents the leading digit(s) and the 'leaf' shows the final digit. It's a quick way to sort data and find the median.
茎叶图在组织数值数据的同时保留了原始数值。‘茎’代表前一位或多位数字，‘叶’显示最后一位数字。这是快速排序数据并找到中位数的好方法。
An ordered stem-and-leaf diagram has leaves arranged in ascending order. Back-to-back stem-and-leaf diagrams compare two related data sets sharing a central stem.
有序茎叶图的叶子按升序排列。背靠背茎叶图共用中间茎，用于比较两组相关数据。
A box plot (or box-and-whisker plot) displays the five-number summary: minimum, Q₁, median, Q₃, and maximum. It shows the spread and skewness of the data. The box spans the IQR, and the whiskers extend to the min and max (unless outliers are marked separately).
箱线图（盒须图）展示五数概括：最小值、Q₁、中位数、Q₃ 和最大值。它显示数据的分布和偏斜程度。箱体覆盖 IQR，须线延伸到最小值和最大值（除非异常值单独标出）。
In AQA Statistics, you may be asked to draw a box plot from given data and compare distributions. Remember to use a scale and label your axis.
在 AQA 统计中，你可能会被要求根据给定数据绘制箱线图并比较分布。记得使用刻度并标记坐标轴。
7. Scatter Graphs & Correlation | 散点图与相关性
A scatter graph shows the relationship between two continuous variables. Each point represents a pair of values. It helps identify patterns or trends.
散点图展示两个连续变量之间的关系。每个点代表一对数值。它有助于发现模式或趋势。
Correlation describes the strength and direction of a linear relationship. Positive correlation means as one variable increases, the other tends to increase. Negative correlation means as one variable increases, the other tends to decrease. No correlation indicates no clear linear pattern.
相关性描述线性关系的强度和方向。正相关表示一个变量增加，另一个也趋向增加。负相关表示一个变量增加，另一个趋向减少。零相关表示没有明显的线性模式。
A line of best fit (trend line) is a straight line drawn through the points on a scatter graph to show the general trend. It should pass as close as possible to most points, with roughly equal numbers of points above and below the line. It is used to make predictions (interpolation within the data range is more reliable than extrapolation beyond it).
最佳拟合线（趋势线）是穿过散点图上各点的直线，用于表示总体趋势。它应尽可能贴近大多数点，线上下的点数大致相等。它用于进行预测（在数据范围内的内插比超出范围的外推更可靠）。
Outliers on a scatter graph may lie far from the general pattern and should be investigated. They can affect the line of best fit.
散点图上的异常值可能远离整体模式，需要加以检查。它们会影响最佳拟合线。
8. Introduction to Probability | 概率入门
Probability is a measure of how likely an event is to happen. It is always a number between 0 and 1, where 0 means impossible and 1 means certain. Probability can also be expressed as a fraction, decimal or percentage.
概率衡量事件发生的可能性大小。它始终是介于 0 到 1 之间的一个数，0 表示不可能，1 表示必然。概率也可以用分数、小数或百分数表示。
An experiment is a repeatable process that gives outcomes, e.g. rolling a die. The sample space is the list of all possible outcomes, often shown in a table or a list. An event is one or more outcomes sharing a characteristic.
试验是一个可重复的过程，会产生结果，例如掷骰子。样本空间是所有可能结果的列表，通常用表格或清单表示。事件是具有某种特性的一个或多个结果。
The probability of an event A is calculated as:
P(A) = number of favourable outcomes / total number of possible outcomes
事件 A 的概率计算如下：
P(A) = 有利结果的数量 / 可能结果的总数
Expected frequency is the number of times you would expect an event to happen in repeated experiments. It is found by multiplying the probability by the number of trials.
预期频数是在重复试验中预期事件发生的次数。由概率乘以试验次数得到。
9. Probability Rules: Mutually Exclusive & Independent Events | 概率法则：互斥事件与独立事件
il on a single coin flip. If A and B are mutually exclusive, then P(A or B) = P(A) + P(B).
互斥事件不能同时发生。例如掷一枚硬币时既出现正面又出现反面。如果 A 和 B 互斥，则 P(A 或 B) = P(A) + P(B)。
When all possible mutually exclusive outcomes are listed, their probabilities sum to 1. This can be used to find the probability of an event not happening: P(not
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