📚 Year 8 CAIE Statistics: Quick Guide to Key Vocabulary and Terminology | Year 8 CAIE 统计：关键词汇术语速记指南
Learning statistics is like discovering a new language. To read graphs, analyse data, and solve probability problems with confidence, you must first master the essential words and phrases. This revision guide breaks down the most important terms you will meet in Year 8 CAIE Statistics, giving you clear definitions in both English and Chinese. Work through each section slowly, and try creating your own example for every term.
学习统计学就像探索一门新语言。要想自信地阅读图表、分析数据并解决概率问题，你首先必须掌握那些核心词汇和短语。这份复习指南将 Year 8 CAIE 统计课程中最重要的术语进行了拆解，为你提供清晰的英文与中文释义。请慢慢地通读每一个部分，并尝试为每个术语自己造一个例句。
1. The Meaning of Statistics | 统计学的含义
Statistics is the science of collecting, organising, presenting, analysing, and interpreting data. It helps us make sense of numbers so we can draw sensible conclusions. In Year 8, you will mostly focus on handling small sets of data by hand and by using simple charts.
统计学是收集、整理、展示、分析和解读数据的科学。它能帮助我们理解数字，从而得出合理的结论。在 Year 8 阶段，你主要学习如何手工或通过简单图表来处理小型数据集。
Data refers to pieces of information, often numbers, that we gather from observations, surveys, or experiments. Before you can work with data, you must know whether it is raw data or processed data. Raw data is the original, unorganised list of values you first write down.
数据指的是我们通过观察、调查或实验收集到的信息片段，通常是数字。在你开始处理数据之前，必须分清楚它是原始数据还是已处理数据。原始数据是指你最初记录下来的、未经整理的数值列表。
2. Types of Data: Qualitative and Quantitative | 数据类型：定性数据与定量数据
Data comes in two main forms. Qualitative data describes qualities or categories, such as eye colour, favourite subject, or car brands. It is non-numerical and often recorded in words. In contrast, quantitative data tells us about quantities and is numerical, like height, test scores, or number of siblings.
数据主要有两种形式。定性数据描述特征或类别，例如眼睛的颜色、最喜欢的科目或汽车品牌。它是非数值型的，通常用文字记录。相反，定量数据告诉我们数量信息，是数值型的，比如身高、考试分数或兄弟姐妹数量。
Within quantitative data, we further split it into discrete and continuous data. Discrete data can only take specific, separate values. For example, the number of students in a class must be a whole number. Continuous data can take any value within a range, such as the mass of an apple or the time taken to run 100 metres.
在定量数据内部，我们又将其细分为离散数据和连续数据。离散数据只能取特定的、相互分离的值。例如，班上的学生数量必须是整数。连续数据则可以取某个范围内的任意值，比如一个苹果的质量或跑完 100 米所用的时间。
3. Population, Sample, and Census | 总体、样本与普查
In statistics, a population is the entire group of people, animals, or things that you want to find out about. Because populations can be very large, we often study a sample, which is a smaller, carefully chosen part of the population. A census happens when you collect data from every single member of the population.
在统计学中，总体指的是你想要了解的全部人群、动物或事物。由于总体可能非常庞大，我们通常会研究样本，即从总体中精心挑选的一部分。而当你能从总体里的每一个成员那里都收集到数据时，这就叫做普查。
Choosing a sample must be done fairly to avoid bias. A biased sample is one that does not represent the population well. For instance, asking only Year 8 boys about the school canteen might miss the views of other year groups and girls. A good sample is random, meaning every member of the population has an equal chance of being picked.
选取样本必须公正，以避免偏差。一个有偏的样本就是不能很好地代表总体的样本。例如，只问 Year 8 的男生对学校食堂的看法，就可能会遗漏其他年级以及女生的意见。一个好的样本通常是随机的，即总体中的每个成员都有相等的机会被选中。
4. Frequency and Frequency Tables | 频数与频数表
Frequency tells you how many times a particular value or category appears in a data set. A frequency table organises data by listing each item or group alongside its frequency. Tally marks, drawn as groups of five, are a fast and accurate way to count frequencies by hand.
频数告诉你某个特定数值或类别在数据集中出现了多少次。频数表通过把每个项目或组别与其频数列在一起来整理数据。画“正”字（以五个为一组）是一种快速且准确的手工计数方法。
To construct a frequency table, first list all possible outcomes in the first column. Then go through your raw data and add one tally for each occurrence. Finally, convert the tallies into numbers in the frequency column. Always add a total row at the bottom to check your counting.
要制作频数表，首先在第一列列出所有可能的结果。然后浏览你的原始数据，每出现一次就画一笔记号。最后，在频数列里把“正”字转换成数字。务必在底部添加“总计”行来核对你的计数。
5. Mean: The Average | 平均数：平均值
The mean is the most common measure of central tendency, often simply called the average. You find it by adding up all the values and then dividing the total by the number of values. The formula is written as:
平均数是最常用的集中趋势度量，通常就简称为平均值。它的计算方法是把所有数值加起来，然后用这个总和除以数值的个数。其公式写作：
Mean = (Sum of all data values) ÷ (Number of data values)
For example, if five friends have pocket money of £4, £5, £5, £6, and £10, the sum is £30. Dividing by 5 gives a mean of £6. Notice how the extreme value of £10 pulls the mean upwards. This is why you should be careful when describing data with outliers.
例如，五位朋友的零花钱分别是 4 英镑、5 英镑、5 英镑、6 英镑和 10 英镑，总和是 30 英镑。除以 5 之后得到平均数为 6 英镑。注意，10 英镑这个极端值把平均数拉高了。这就是为什么当数据包含异常值时，你在描述数据时要格外小心。
6. Median and Mode | 中位数与众数
The median is the middle value when you arrange all numbers in order from smallest to largest. If there are two middle numbers, the median is the mean of those two. The median is unaffected by extremely high or low values, so it often gives a better picture of a typical value when data is skewed.
中位数是当你把所有数字从小到大排列时，位于正中间的那个数值。如果有两个中间数，中位数就是它们的平均数。中位数不受极端高值或低值的影响，因此当数据偏斜时，中位数往往更能代表典型值。
The mode is the value that appears most often. A data set can have one mode, more than one mode, or no mode at all if all values appear equally often. The mode is especially useful for qualitative data. For example, if most students in a class chose 'blue' as their favourite colour, blue is the modal category.
众数是出现次数最多的数值。一个数据集可能有一个众数、多个众数，或者在所有数值都出现同样次数时没有众数。众数对于定性数据特别有用。例如，如果班上大多数学生都选择了“蓝色”作为最喜欢的颜色，那么“蓝色”就是众数类别。
7. Range: A Measure of Spread | 极差：一种离散度量
Range tells you how spread out the data values are. You find it by subtracting the smallest value from the largest value. A large range means the data is very spread out, while a small range means the data is tightly clustered.
极差告诉你数据的分散程度。它的计算方法是用最大值减去最小值。极差很大说明数据很分散，极差很小则说明数据很集中。
Range = Largest value – Smallest value
Imagine two Year 8 classes took the same maths test. Class A had scores from 42 to 98, giving a range of 56 marks. Class B had scores from 66 to 80, giving a range of only 14 marks. Class A's results are much more varied, which might prompt the teacher to look for reasons behind such big differences.
假设两个 Year 8 班级参加了同样的数学考试。A 班的分数从 42 分到 98 分，极差为 56 分。B 班的分数从 66 分到 80 分，极差仅为 14 分。A 班的成绩差异要大得多，这可能促使老师去探究如此大差距背后的原因。
8. Probability Vocabulary | 概率词汇
Probability measures how likely an event is to happen. It always ranges from 0 to 1, where 0 means impossible and 1 means certain. You can write probability as a fraction, a decimal, or a percentage. Words like 'even chance', 'likely', and 'unlikely' also appear in exam questions.
概率衡量一个事件发生的可能性有多大。它的取值总是在 0 到 1 之间，0 表示不可能发生，1 表示必然发生。你可以用分数、小数或百分数来书写概率。像“对等机会”、“很可能”和“不太可能”这些词也会出现在考题中。
An experiment is a repeatable process that gives results, such as rolling a dice. An outcome is a single possible result, like rolling a 3. An event is a set of one or more outcomes that you are interested in, for instance rolling an even number. The sample space is the list of all possible outcomes, usually shown inside curly brackets.
试验是一个可重复、且能产生结果的过程，比如掷骰子。结果指的是一个单一的可能结果，如掷出 3 点。事件则是你感兴趣的一个或多个结果的集合，例如掷出偶数。样本空间是所有可能结果的列表，通常用大括号列出。
9. Charts and Graphs: Bar Charts and Pictograms | 图表：条形图和象形图
A bar chart uses rectangular bars to represent frequencies. The bars must be of equal width and there should be gaps between them to show the categories are separate. The height or length of each bar matches the frequency of that category. Always label both axes clearly and give the chart a title.
条形图使用矩形长条来表示频数。长条必须等宽，并且长条之间要有空隙，以表明这些类别是相互独立的。每个长条的高度或长度要对应那个类别的频数。务必清晰标明两根坐标轴并为图表加上标题。
A pictogram uses small pictures or symbols to represent data. You must first decide what each symbol stands for, and then draw the correct number of symbols for each category. A key is essential to show the scale, and you may need to draw half or part of a symbol to show numbers that are not exact multiples.
象形图使用小图片或符号来表示数据。你必须先确定每个符号代表什么，然后为每个类别画出正确数量的符号。图例至关重要，它用以说明符号代表的数值尺度；遇到不是精确倍数的数字时，你可能需要画出半个或部分符号。
10. Pie Charts and Line Graphs | 饼图与折线图
A pie chart is a circle divided into sectors, where each sector represents a proportion of the whole. The size of the angle at the centre of each sector is proportional to the frequency it represents. To draw a pie chart by hand, you must calculate how many degrees each category deserves, remembering that the whole circle is 360°.
饼图是一个被分割成若干扇形的圆，每个扇形代表整体的一部分。每个扇形在圆心处的角度大小与其所代表的频数成正比。要手工绘制饼图，你必须先计算出每个类别对应多少度，并记住整个圆是 360°。
Sector angle = (Category frequency ÷ Total frequency) × 360°
A line graph is used to show how data changes over time. You plot points and join them with straight lines. The horizontal axis often shows time, and the vertical axis shows the quantity being measured. Line graphs are excellent for spotting trends, such as rising or falling temperatures over a week.
折线图用于展示数据如何随时间变化。你标出各个数据点并用直线将它们连接起来。横轴通常表示时间，纵轴表示被测量的量。折线图非常适合用来发现趋势，比如一周内温度的上升或下降。
11. Interpreting Data: Trends and Comparisons | 数据解读：趋势与比较
Once you have drawn a graph, you must be able to describe what it shows. Look for the highest and lowest values, any overall increase or decrease, and any unusual spikes or dips. Use phrases like 'the trend is upwards', 'it reached a peak', or 'there was a steady decline' to make your description precise.
一旦你画好了图表，你就必须能够描述出它所展示的内容。要找出最高值和最低值、任何整体的上升或下降趋势，以及任何不寻常的峰值或低谷。可以使用一些短语，比如“趋势是向上的”、“它达到了顶峰”或“出现了稳步下滑”，以使你的描述更加精确。
When comparing two sets of data, always refer to their shapes, centres, and spreads. You might say one median is higher than the other, or that one data set has a much larger range. A good comparison quotes numbers from the graph or table to back up every statement you make.
当比较两组数据时，始终要提及它们的形状、中心和分散程度。你可以说一组的中位数比另一组高，或者一组数据的极差大得多。出色的比较会引用图表或表格中的具体数字来支持你做出的每一个陈述。
12. Exam-Style Command Words | 考试常见指令词
CAIE questions often contain specific command words that tell you exactly what to do. 'State' means give a short, clear answer without explanation. 'Calculate' means work out the answer and show your steps. 'Describe' means say what you see in the data or on the chart, mentioning key features and figures.
CAIE 考题中常常包含特定的指令词，它们会精确地告诉你该做什么。“陈述”意味着给出简短清晰的答案，无需解释。“计算”意味着算出答案并展示你的步骤。“描述”意味着说出你在数据中或图表上看到了什么，要提及关键特征和数字。
'Compare' asks you to look at similarities and differences, often between two data sets. You must write about both sets and use comparative words like 'higher', 'lower', or 'more consistent'. 'Explain' goes one step further: you must give reasons for why something happens, linking your reasoning back to the numbers or the context.
“比较”要求你关注相似与不同之处，通常是在两组数据之间。你必须同时写到两组数据，并使用如“更高”、“更低”或“更稳定”这样的比较性词语。“解释”则更进一步：你必须给出某事发生的原因，并将你的推理联系回那些数字或背景。
Published by TutorHao | Statistics Revision Series | aleveler.com
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