📚 Year 8 Cambridge Statistics: Quick Memorisation Guide to Key Terms | Year 8 剑桥统计：关键术语速记指南
In Year 8 Cambridge Statistics, mastering the language of data is your first step towards confident problem-solving. Whether you are calculating averages, drawing a pie chart, or discussing the chance of rain, the right terms will help you think and communicate like a statistician. This guide breaks down the most important vocabulary into bite‑sized sections, complete with memory tricks and paired English‑Chinese explanations, so you can recall every term when it counts.
在 Year 8 剑桥统计课程中，掌握数据的语言是自信解题的第一步。无论是计算平均数、画饼图，还是讨论下雨的可能性，正确的术语都能帮你像统计学家一样思考和表达。这份指南将最重要的词汇拆分成易于消化的小节，并配有记忆技巧和中英配对解释，让你在需要时随时想起每一个术语。
1. Measures of Central Tendency | 集中趋势测度
The mean is what many people call the 'average'. You find it by adding all the values together and dividing by the number of values. Think of 'mean' as the 'sharing fairly' number – if everyone got the same amount, that would be the mean.
平均数就是很多人所说的“平均值”。你把所有数值加起来，再除以数值的个数就能得到。可以把“mean”想成“公平分配”的数值——如果每个人都得到同样多的量，那个量就是平均数。
The median is the middle value when the data is sorted from smallest to largest. If there are two middle values, you take the mean of those two. A handy trick: 'median' sounds like 'medium', and it sits in the middle of the set.
中位数是将数据从小到大排列后处于中间位置的值。如果有两个中间值，就取它们的平均数。一个小窍门：“median”听起来像“medium（中间）”，它正好坐在数据集的中间。
The mode is the value that appears most often. It is the 'most popular' number. You can remember it because 'mode' and 'most' both start with 'mo'. A set of data can have one mode, more than one mode, or no mode at all.
众数是出现次数最多的值，也就是“最受欢迎”的数字。你可以这样记：“mode”和“most（最多）”都以“mo”开头。一组数据可以有一个众数、多个众数，也可能没有众数。
2. Measures of Spread | 离散测度
The range tells you how spread out the data are. Subtract the smallest value from the largest value. A small range means the numbers are close together; a large range means they are far apart. Picture a mountain range – the peaks are far apart if the range is big.
极差告诉你数据分布有多宽。用最大值减去最小值即可。极差小说明数字比较集中；极差大说明数字分散得很开。想象一条山脉（range），如果范围很大，山峰之间就离得很远。
While the range is quick to calculate, it only uses two numbers and can be affected by extreme values, often called outliers. An outlier is a piece of data that sits far away from the rest of the group. Knowing the range together with the mean and median gives a much better picture of the data.
极差计算起来很快，但它只用了两个数，容易受极端值（常常被称为异常值）的影响。异常值就是远离其他数据的那个点。把极差和平均数、中位数结合起来看，才能更好地了解数据全貌。
3. Data Types and Collection | 数据类型与收集
Data can be categorical or numerical. Categorical data are described by labels or names, like favourite colour or type of pet. Numerical data are numbers that you can measure or count, such as height, age, or number of siblings. To keep things tidy, remember: cat‑egorical data are categories.
数据可以分为类别数据和数值数据。类别数据用标签或名称来描述，比如最喜欢的颜色或宠物种类。数值数据是你可以测量或计数的数字，比如身高、年龄或兄弟姐妹的数量。为了好记：类别（categorical）数据就是分成各种“类别”的数据。
When we gather information, we must think about whether it is primary data (collected by you for a specific purpose, like a survey you design) or secondary data (collected by someone else, like data from a government website). The word 'primary' reminds you it comes first-hand.
在收集信息时，我们要分清这是一手数据（你为了特定目的自己收集的，比如你自己设计的调查问卷），还是二手数据（别人收集好的，比如政府网站上的数据）。“一手”（primary）这个词提醒你，它来自第一手来源。
4. Frequency and Frequency Tables | 频数与频数表
Frequency is simply the number of times something happens or appears. In a tally, each group of five is marked with a diagonal line through the first four, making counting easy. A frequency table organises data into categories along with their frequencies.
频数就是某个事件发生或某个项目出现的次数。在画“正”字计数时，每五个为一组，前四个是竖线，第五个是斜线，这样数起来很方便。频数表把各类别及其频数整理在一起。
You can also calculate a relative frequency, which is the frequency of a category divided by the total number of observations. This is often written as a fraction, decimal, or percentage. Understanding frequency tables helps you move smoothly into drawing bar charts and pie charts.
你还可计算相对频数，即某个类别的频数除以总观测次数。这通常写成分数、小数或百分数。理解频数表有助于你顺利过渡到绘制条形图和饼图。
5. Bar Charts and Pictograms | 条形图与象形图
A bar chart uses rectangular bars to show the frequency of categories. The bars have equal width and should not touch each other, because the categories are separate. The length of each bar represents the frequency. Label your axes clearly and give the chart a title.
条形图用长方形条块表示各类别的频数。条块的宽度相等，互相之间不应接触，因为类别是分开的。条块的长度代表频数。要清晰地标注坐标轴，并给图表加上标题。
A pictogram uses small pictures or symbols to represent data. Each picture stands for a certain number of items. Always check the key that tells you what one symbol is worth. For example, one cake icon could represent 2 cakes sold. Pictograms are eye‑catching but can be tricky when the symbol needs to be cut in half.
象形图用小图片或符号来呈现数据。每个图片代表一定数量的物品。一定要查看图例，它会告诉你一个符号代表多少。例如，一个蛋糕图标可能代表卖出了2个蛋糕。象形图很吸引眼球，但遇到需要切半的符号时就有点麻烦。
6. Pie Charts and Percentages | 饼图与百分比
A pie chart is a circle divided into sectors, where each sector represents a proportion of the whole. To draw a pie chart, you often convert frequencies into angles. Since a full circle is 360°, you multiply each proportion by 360°. Think of a pie that you slice according to how much each friend has contributed – the bigger the share, the larger the slice.
饼图是一个被划分成扇形的圆，每个扇形代表整体的一部分。画饼图时，常常要把频数转换为角度。因为一个整圆是360°，你就把每个比例乘以360°。想象一个馅饼，你根据每个朋友贡献的多少来切——贡献越多，分到的块儿越大。
Percentages are essential here. Percentage means 'out of 100'. To find a percentage from a fraction, multiply by 100. A quick tip: ‘cent’ in percent refers to 100, like century or centipede. When comparing pie charts, always check the total number of observations – a 50% slice in a survey of 200 people means something different from 50% in a survey of 20 people.
百分比在这里很重要。百分比的意思是“每一百份中的份数”。要把分数化成百分比，乘以100即可。小窍门：“percent”中的“cent”指100，就像世纪（century）或蜈蚣（centipede）一样。比较饼图时，一定要留意观测总数——一个200人调查中的50%扇区，和一个20人调查中的50%扇区，含义是不同的。
7. Scatter Plots and Correlation | 散点图与相关性
A scatter plot (or scatter graph) shows the relationship between two sets of numerical data. One variable goes on the horizontal x‑axis, the other on the vertical y‑axis. Each dot represents a paired observation, like a person's height and arm span.
散点图显示两组数值数据之间的关系。一个变量放在横轴（x轴）上，另一个放在纵轴（y轴）上。每个点代表一对观察值，比如一个人的身高和臂展。
Correlation describes the pattern we see. A positive correlation means that as one variable increases, the other tends to increase – the points slope upwards. A negative correlation means that as one variable increases, the other tends to decrease – the points slope downwards. If the points are scattered randomly with no clear pattern, we say there is no correlation. The word 'correlation' contains 'co' (together) and 'relation', so two things are related together.
相关性描述了我们看到的模式。正相关意味着一个变量增大时，另一个也倾向于增大——点群向上倾斜。负相关意味着一个变量增大时，另一个反而倾向于减小——点群向下倾斜。如果点随机散落，没有明显的模式，我们就说没有相关性。“correlation”这个词含有“co”（共同）和“relation”（关系），所以是两个事物一起关联变化。
8. Probability Basics | 概率基础
Probability is a measure of how likely an event is to happen. It is always a number between 0 and 1. A probability of 0 means impossible; a probability of 1 means certain. Often, probability is expressed as a fraction: (number of favourable outcomes) ÷ (total number of possible outcomes).
概率是衡量一个事件发生的可能性有多大的量。它总是在0到1之间的一个数字。概率为0表示不可能；概率为1表示必然发生。概率常常用分数表示：（有利结果的数量）÷（所有可能结果的总数）。
We use words like impossible, unlikely, even chance, likely and certain to describe probability on a verbal scale. The expression 'fifty‑fifty' means an even chance, or a probability of 0.5. Try this memory picture: the word 'probability' starts like 'probable', and a probable rain means likely to rain.
我们用不可能、不太可能、均匀机会、可能和一定等词语来描述概率的语言标尺。“五五开”表示均匀机会，即概率为0.5。试试这个记忆画面：“probability”和“probable（很可能的）”开头一样，一场“probable rain”就是很可能要下雨。
9. Sample Space and Events | 样本空间与事件
The sample space is the set of all possible outcomes of an experiment. For a single coin toss, the sample space is {Heads, Tails}. When you roll a fair six‑sided die, the sample space is {1, 2, 3, 4, 5, 6}. Think of a 'space' that contains every possibility.
样本空间是一次实验所有可能结果的集合。对一次抛硬币来说，样本空间是 {正面，反面}。当你掷一枚公平的六面骰子时，样本空间是 {1, 2, 3, 4, 5, 6}。想象一个“空间”，里面装着每一种可能。
An event is a set of outcomes that you are interested in. For example, 'rolling an even number' f an event = (number of outcomes in the event) ÷ (number of outcomes in the sample space).
事件是你所关注的一组结果。例如，“掷出偶数”是一个事件，它包含结果 2、4、6。事件可以是简单的（一个结果）或复合的（多于一个结果）。事件的概率 = (事件包含的结果数) ÷ (样本空间中的结果总数)。
10. Random Experiments and Fairness | 随机实验与公平性
A random experiment is one where you know all the possible outcomes, but you cannot predict which one will occur. Tossing a fair coin is random because you cannot tell whether you will get heads or tails on the next throw, even though you know the possible outcomes.
随机实验是指你知道所有可能的结果，但无法预测哪一個结果会发生的实验。抛一枚公平硬币就是随机的，因为你虽然知道可能的结果，却无法知道下一次会得到正面还是反面。
Objects like dice and coins are fair when every outcome has the same chance of happening. A fair coin has a ½ probability of heads and ½ probability of tails. If a die is loaded so that it lands on six more often, it is biased. The word 'fair' gives you the idea of equal treatment, just like sharing sweets fairly.
当每个结果发生的机会都相等时，像骰子和硬币这样的物件就是公平的。一枚公平硬币出现正面的概率是 ½，反面的概率也是 ½。如果一个骰子被做了手脚，导致它更常出现六点，那它就是有偏的。“公平”（fair）这个词给你一种待遇相同的概念，就像公平地分享糖果。
11. Relative Frequency and Experimental Probability | 相对频数与实验概率
When we actually perform an experiment many times, we can calculate the relative frequency of an event: (number of times the event occurs) ÷ (total number of trials). As the number of trials increases, the relative frequency often gets closer to the theoretical probability. This is sometimes called the experimental probability.
当我们真的把一个实验做了许多次，就可以计算某事件的相对频数：（事件发生的次数）÷（试验总次数）。随着试验次数增加，相对频数往往会趋近于理论概率。这有时被称为实验概率。
, which is close to 0.5. The gap between experimental and theoretical probability helps us understand the role of chance and small sample sizes.
例如，如果抛硬币100次，得到47次正面，正面的实验概率就是 47/100 = 0.47，这很接近 0.5。实验概率和理论概率之间的差距，能帮助我们理解随机性和小样本量的作用。
12. Quick Tips for Memorising Statistical Terms | 统计术语速记小贴士
Make a set of flashcards with the term on one side and the definition and an example on the other. Colour‑code them: blue for averages, green for graphs, orange for probability. Use silly sentences to lock tricky words in your mind, like 'The MEAN teacher adds up all the marks and divides fairly' or 'The MEDIAN sits in the MIDDLE like a quiet meditator'.
制作一套抽认卡，一面写术语，另一面写定义和例子。给卡片按颜色分类：蓝色表示平均数，绿色表示图表，橙色表示概率。用一些滑稽的句子把难记的词锁在脑子里，比如“MEAN（平均数）老师会把所有分数加起来再公平地除开”，或者“MEDIAN（中位数）像个安静的冥想者坐在中间”。
Draw mind maps that connect related ideas. Place 'Data' in the centre and branch out to 'Measures', 'Graphs', 'Probability'. This visual layout mirrors the structure of this guide and helps your brain see the whole picture.
绘制思维导图，把相关的概念连接起来。把“数据”放在中心，分出“测度”、“图表”、“概率”等分支。这种视觉布局就像本指南的结构一样，能帮助你的大脑看见全貌。
Published by TutorHao | Statistics Revision Series | aleveler.com
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