📚 Year 8 AQA Statistics: Vocabulary Memorisation Guide | AQA Year 8 统计：词汇术语速记指南
In Year 8 AQA Statistics, a solid command of subject vocabulary makes the difference between guessing and knowing. This guide organises essential terms into bite-sized sections, pairs every English definition with a clear Chinese translation, and adds memory hacks to speed up your learning. Keep it handy for homework, revision, and building the confidence to explain data like a true statistician.
在 AQA Year 8 统计课程中，扎实的术语功底决定了你是“靠猜”还是“真懂”。这份指南将核心词汇拆分成易于消化的小板块，为每条英文定义配上了清晰的中文翻译，还加入了记忆技巧，帮你加快学习进度。用它来辅助作业、复习，让你像真正的统计学家一样自信地解读数据。
1. The Three Averages: Mean, Median and Mode | 三种平均数：均值、中位数与众数
The mean is the arithmetic average. Add up all the data values, then divide by the number of values. It is sensitive to every number in the set.
均值是算术平均数。把所有数据值加起来，再除以数据的个数。它对数据集中的每一个数值都很敏感。
Memory trick: “Mean has a green heart—it shares the total equally.” (Imagine a mean character turning generous.)
记忆诀窍：“均值有一颗绿色公平心，总数平分。”（想象一个刻薄的角色突然变得大方。）
The median is the middle value when the data are arranged in order. If there is an even number of items, the median is the mean of the two central numbers.
中位数是将数据按顺序排列后处于中间位置的数值。如果数据的个数是偶数，中位数就是中间两个数的均值。
Tip: “Median marches into the middle of the lineup, unmoved by extremes.”
窍门：“中位数走到队伍正中间，不受极端值影响。”
The mode is the value that appears most often. A dataset may have one mode, more than one mode (bimodal or multimodal), or no mode at all if all values appear equally often.
众数是出现次数最多的数值。一组数据可能有一个众数、多个众数（双众数或多众数），如果所有数值出现次数相同则没有众数。
Think of mode as “the most fashionable”—like the style everyone is wearing.
把众数想成“最流行款式”——就像大家纷纷效仿的潮流。
Mean = Σx ÷ n
中位数：居中者
2. Range: Measuring the Spread | 范围：衡量分散程度
The range tells you how far apart the whiskers of the data spread. It is simply the largest value minus the smallest value.
范围表示数据分布从最低到最高的跨度。它简单地用最大值减去最小值。
A small range means the data points huddle close together; a large range signals they are stretched out over a wide interval.
范围小意味着数据点紧密聚集在一起；范围大则表明它们拉开了很宽的间隔。
Visual memory: “Range runs the entire roller coaster track, from the lowest dip to the highest climb.”
形象记忆：“范围跑完整条过山车轨道，从最低俯冲到最高攀升。”
Range = Largest value – Smallest value
3. Probability Vocabulary: From Impossible to Certain | 概率词汇：从不可能到必然
Probability describes how likely an event is to happen, measured on a scale from 0 to 1. Words like ‘impossible’, ‘unlikely’, ‘even chance’, ‘likely’ and ‘certain’ give snapshot labels for this scale.
概率描述一个事件发生的可能性有多大，用 0 到 1 的尺度来衡量。像“不可能”“不太可能”“等可能”“很可能”“必然”这些词语就是为了快速标记这个尺度。
0 represents impossible (e.g., flying by flapping arms); 1 represents certain (e.g., the sun will rise tomorrow). An even chance sits exactly at ½, like flipping a fair coin.
0 表示不可能（如挥动手臂飞天）；1 表示必然（如太阳明天升起）。等可能恰好位于 ½，类似抛一枚均匀硬币。
Key terms: outcome (a single result), event (a collection of outcomes), sample space (all possible outcomes).
关键术语：outcome（一个结果），event（一组结果组成的集合），sample space（所有可能结果的集合）。
Memory ladder: “0 – Impossible, ¼ – Unlikely, ½ – Even chance, ¾ – Likely, 1 – Certain.”
记忆阶梯：“0——不可能，¼——不太可能，½——等可能，¾——很可能，1——必然。”
4. Statistical Graphs: Which Chart Tells What? | 统计图表：什么图说什么事
Bar charts display categorical data with rectangular bars whose lengths represent frequency. Keep bars separate to show distinct categories.
条形图用矩形条展示分类数据，条的长度代表频数。条形之间要留空隙，表示不同类别。
Pictograms use icons to show frequencies; each picture stands for a certain number of items, and a key explains the scale.
象形图用图标来表示频数；每个图画代表一定数量的物品，图例说明比例。
Pie charts show proportions of a whole. Each slice has a central angle that mirrors the category’s relative frequency. The whole circle is 360°.
饼图展示整体各部分的比例。每一扇形的圆心角对应类别的相对频率。整个圆是 360°。
Line graphs connect data points with straight lines, commonly used to show trends over time. Scatter graphs plot two sets of variables as points, revealing relationships or correlations.
折线图用直线连接数据点，常用于显示随时间变化的趋势。散点图把两组变量的数值以点的形式标出，揭示它们之间的关系或相关性。
Quick recall: “Bar for categories, pie for parts, line for changes, scatter for connections.”
快速回忆：“类别用条，部分用饼，变化用线，关系用散点。”
5. Data Collection: Primary vs Secondary | 数据收集：一手数据与二手数据
Primary data is information you collect yourself for a specific purpose, such as conducting a survey or timing how long a phone holds charge.
一手数据是你为了特定目的亲自收集的信息，例如实施问卷调查或计时手机续航时间。
Secondary data is information gathered by someone else, like statistics from websites, newspapers, or a government census. It is quicker to obtain but may not fit your question exactly.
二手数据是别人已经收集好的信息，比如来自网站、报纸或政府人口普查的统计数据。它获取更快，但不一定恰好匹配你的问题。
Data can also be categorical (qualitative), describing names or labels, or numerical (quantitative), consisting of numbers. Numerical data splits further into discrete and continuous.
数据还可以分为分类数据（定性），描述名称或标签；或数值数据（定量），由数字构成。数值数据可进一步分为离散和连续。
Common collection tools: questionnaire (set of written questions), interview (spoken questions), observation (watching and recording).
常见收集工具：问卷（一套书面问题）、访谈（口头提问）、观察（观看并记录）。
6. Frequency and Tallying | 频数与画记
Frequency is the number of times a particular data value or category occurs. Tally marks help you count systematically; each vertical stroke after the fourth crosses the previous four (~~III~~) to make a bundle of five.
频数是某个特定数据值或类别的出现次数。画记符号帮你系统计数；每画满四条竖线后，第五画以横线划过前四条（正），形成一个五的捆。
A frequency table organises raw data into a neat list of categories alongside their frequencies. It often includes a tally column before the final count.
频数表将原始数据整理成清晰的列表，列出各类别及其对应的频数。在最终计数之前通常还有一个画记列。
For continuous data, a grouped frequency table bundles values into intervals (e.g., 10–19, 20–29) so patterns can be seen.
对于连续数据，分组频数表把数值归入区间段（如 10–19, 20–29），以便观察分布模式。
| Favourite Colour | Tally | Frequency |
|---|---|---|
| Red | ~~III~~ | 5 |
| Blue | ~~III~~ I | 6 |
| Green | III | 3 |
Small table example: Favourite Colour survey with tally and frequency. 中文示例：最喜爱颜色调查的频数表。
7. Discrete and Continuous Data | 离散数据与连续数据
Discrete data can only take specific, separate values—often things you count, such as the number of pencils in a case or goals scored in a match. There are no in-between values.
离散数据只能取特定的、分开的数值——通常是可以数出来的量，例如铅笔盒里的铅笔数量或一场比赛的进球数。这些数值之间没有中间值。
Continuous data can take any value within a range—it is measured, not counted. Height, mass, and time are continuous because they can fall anywhere along a scale (e.g., 1.63 m).
连续数据可以在一个范围内取任意值——它是测量出来的，不是数出来的。身高、质量和时间都是连续数据，因为它们可以落在量尺上的任何位置（例如 1.63 米）。
Check trick: if you can answer “How many?” and the answer is a whole number, it’s probably discrete. If you ask “How much?” and a decimal is possible, it’s continuous.
检验技巧：如果你问“多少个？”，答案通常是整数，那很可能是离散的。如果你问“多少？”，答案可能出现小数，那就是连续的。
Shoe size can be confusing—although it looks like a number, it only appears in half- or full-size steps, so it is treated as discrete in most school contexts.
鞋码可能会让你困惑——尽管它看起来是个数，但它只出现在半码或整码的阶梯上，因此在大多数学校情境中被视作离散数据。
8. Population and Sample | 总体与样本
The population is the entire set of individuals or items that you are interested in studying. It could be all students in your school, every apple on a tree, or all cars registered in a city.
总体是你感兴趣研究的所有个体或物件组成的完整集合。它可以是你学校所有的学生、一棵树上的所有苹果，或一个城市登记的所有汽车。
A sample is a smaller, manageable subset taken from the population to represent it. Because surveying the whole population is often time-consuming or expensive, a well-chosen sample can give reliable answers.
样本是从总体中抽出的一个较小的、便于处理的子集，用来代表总体。由于调查整个总体通常耗时耗力，一个精心选择的样本可以给出可靠的答案。
A random sample is one where every member of the population has an equal chance of being selected, reducing bias. Bias means the sample does not fairly represent the population, leading to skewed conclusions.
随机样本是指总体中每个成员都有同等机会被选中的样本，这可以减少偏差。偏差意味着样本没有公平地代表总体，导致结论偏颇。
Memory: “Population is the whole family photo; sample is the few people you actually ask.”
记忆：“总体是全家福照片；样本是你真正去问的那几个人。”
9. Correlation and Scatter Graphs | 相关与散点图
Correlation describes the direction and strength of a relationship between two sets of data on a scatter graph. The points form a pattern that can be positive, negative, or show no correlation.
相关描述了散点图上两组数据之间关系的方向和强度。数据点形成的模式可以是正相关、负相关，或没有相关性。
Positive correlation: as one variable increases, the other tends to increase. On a scatter graph, points slope upwards from left to right (like height and shoe size).
正相关：当一个变量增加时，另一个也倾向于增加。散点图上，点从左到右向上倾斜（例如身高和鞋码）。
Negative correlation: as one variable increases, the other tends to decrease. Points slope downwards from left to right (like the age of a car and its value).
负相关：当一个变量增加时，另一个倾向于减少。点从左到右向下倾斜（例如车龄和车价）。
No correlation means the points are scattered randomly with no obvious upward or downward pattern. A line of best fit can be drawn through correlated points to summarise the trend.
无相关意味着点随机散布，没有明显的向上或向下模式。最佳拟合线可以画在具有相关性的点中以总结趋势。
Outlier: a data point that lies far away from the general pattern. It should be investigated but not automatically removed.
离群值：一个远离整体模式的数据点。应加以考察，但不自动删除。
Correlation does not mean causation.
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