📚 Year 9 CAIE Statistics: A Rapid Vocabulary and Terminology Memorisation Guide | 九年级CAIE统计：词汇术语速记指南
Mastering the core statistical vocabulary is the first step to confidently tackling data analysis and probability in Year 9 CAIE Mathematics. This guide breaks down the essential terms into twelve short, exam-focused sections, pairing every English definition with a Chinese equivalent, and adds memory aids, formula reminders and common traps so that you can recall the right word at the right moment.
掌握核心统计词汇是自信应对九年级CAIE数学中数据分析和概率的第一步。本指南把必备术语拆成十二个紧扣考点的小节，每个英文定义都配有中文对照，并加入记忆口诀、公式提示和常见陷阱，帮助你在考场上第一时间想起正确的词。
1. Why Vocabulary Comes First | 为什么词汇要优先掌握
Statistics questions in Year 9 CAIE papers are word-heavy. A single instruction such as 'describe the distribution', 'compare the two sets of data' or 'give a reason why the sample may be biased' can carry three or four marks, and those marks are awarded for using the correct statistical term, not for a long explanation. If you do not know what 'biased' or 'distribution' means, you cannot answer at all.
九年级CAIE试卷中的统计题文字量很大。一句指令如"描述该分布""比较这两组数据""说明该样本可能存在偏差的原因"，往往就是三到四分，而这些分数是给"用了正确统计术语"的答案，而不是给长篇大论。如果你不认识 biased（偏差）或 distribution（分布），就根本无从下笔。
There are three layers of vocabulary you need. First, the naming layer: words that classify data, such as qualitative, quantitative, discrete and continuous. Second, the summarising layer: words that describe a data set, such as mean, median, mode, range and interquartile range. Third, the commenting layer: words you use to write a conclusion, such as correlation, consistent, spread, outlier and approximately. Examiners reward all three layers.
你需要三个层次的词汇。第一是"命名层"：用来给数据分类的词，如 qualitative（定性）、quantitative（定量）、discrete（离散）、continuous（连续）。第二是"概括层"：用来描述一组数据的词，如 mean（均值）、median（中位数）、mode（众数）、range（极差）、interquartile range（四分位距）。第三是"评述层"：写结论时用的词，如 correlation（相关性）、consistent（稳定的）、spread（离散程度）、outlier（异常值）、approximately（大约）。三个层次都是给分点。
The most reliable method is to learn terms in pairs and in context. Never memorise a word on its own: always attach it to a one-line definition and a tiny example, for instance 'discrete - you can count it - number of goals in a match'. Memory works far better when a word is stored with a picture and a number.
最可靠的方法是"成对＋带情境"记忆。绝不要孤立地背单词：一定要给它配一句定义和一个小例子，例如"discrete——可以数——一场比赛的进球数"。当单词与画面和数字一起存入记忆时，回忆效率会高得多。
2. Data and Its Types | 数据及其类型
ualitative data, also called categorical data, describes a quality or a category: eye colour, type of car, favourite subject, month of birth. It cannot sensibly be added or averaged, even if it is coded with numbers such as 1 = red and 2 = blue.
数据是为分析而收集的信息。你必须掌握的第一个分类是定性数据与定量数据。定性数据（也称分类数据）描述的是性质或类别：眼睛颜色、汽车类型、最喜欢的科目、出生月份。即使给它编码成数字（1＝红色，2＝蓝色），也不能合理地进行加法或求平均。
Quantitative data, also called numerical data, involves numbers that measure or count something: height, mass, temperature, test score, number of siblings. Only quantitative data can be summarised with a mean, and only quantitative data can be plotted on a histogram or a scatter graph.
定量数据（也称数值数据）涉及可以度量或计数的数字：身高、质量、温度、考试分数、兄弟姐妹人数。只有定量数据才能用均值概括，也只有定量数据才能画直方图或散点图。
| Term | 术语 | Definition | 定义 | Example | 例子 |
| Qualitative / Categorical 定性／分类 | Describes a quality or category 描述性质或类别 | Eye colour, transport to school 眼睛颜色、上学交通方式 |
| Quantitative / Numerical 定量／数值 | Involves numbers that can be counted or measured 可以计数或度量的数字 | Height, test score 身高、考试分数 |
| Discrete 离散 | Countable, usually whole numbers 可数，通常为整数 | Number of students 学生人数 |
| Continuous 连续 | Measured on a scale, any value in a range 在刻度上测量，可取区间内任意值 | Weight, time 体重、时间 |
Exam trap: if a question says 'state the type of data', it wants one of the four words above, not a sentence. If it says 'give a reason', you must justify it: 'number of goals is discrete because it can be counted'.
考试陷阱：如果题目说"说出数据的类型"，答案只能是上面四个词之一，不要写成句子。如果说"给出理由"，就必须解释："进球数是离散的，因为它可以数出来。"
3. Discrete and Continuous Data | 离散数据与连续数据
Quantitative data splits further into discrete data and continuous data. Discrete data can only take particular, separate values, usually whole numbers, and there are gaps between the values. Continuous data can take any value within a range, and the values form an unbroken scale with no gaps.
定量数据进一步分为离散数据与连续数据。离散数据只能取特定、分离的值，通常是整数，取值之间有间隔。连续数据可以取某个范围内的任意值，数值构成连续不断的刻度线，没有间隔。
The one-line rule to remember is: discrete means you count it, continuous means you measure it. A useful test is to ask whether a halfway value makes sense. '2.5 students' is nonsense, so number of students is discrete; '2.5 kilograms' is perfectly possible, so mass is continuous.
要记住的一句话规则是：discrete 是"数出来的"，continuous 是"量出来的"。一个好用的检验方法是问"中间值是否说得通"。"2.5个学生"毫无意义，所以学生人数是离散的；"2.5千克"完全可能，所以质量是连续的。
- Discrete examples: number of cars in a car park, number of goals in a match, shoe size, number of pets, dice score.
离散数据的例子：停车场里的汽车数、一场比赛的进球数、鞋码、宠物数量、骰子点数。 - Continuous examples: height, weight, temperature, time taken, length of a leaf, amount of rainfall.
连续数据的例子：身高、体重、温度、所用时间、叶片长度、降雨量。 - Common trap: shoe size and temperature are the classic exceptions. Shoe size goes 5, 5.5, 6 and is treated as discrete in most school questions; temperature is treated as continuous because it is read from a scale.
常见陷阱：鞋码和温度是经典例外。鞋码是 5、5.5、6 这样跳着走的，多数校园题目当作离散；温度从刻度上读出，当作连续。 - Money is normally treated as continuous because it is measured on a scale, though counting coins can be described as discrete.
金钱通常按连续数据处理，因为它是在刻度上度量的；但数硬币可以描述为离散。
Being able to name the data type also tells you which graph to draw: discrete data is shown with a bar chart or a bar-line graph, while continuous data is shown with a histogram or a cumulative frequency curve.
能说清数据类型，也就决定了该画什么图：离散数据用条形图或条形折线图，连续数据用直方图或累积频数曲线。
4. Population, Sample and Census | 总体、样本与普查
These three words form the backbone of every data-collection question. Population means the whole group of items or people you are studying - not necessarily people, and not necessarily a country. Sample means a smaller part of the population that you actually collect data from, used to make an estimate about the population. Census means collecting data from every single member of the population, with no sampling at all.
这三个词是每道数据收集题的骨架。Population（总体）指你研究的所有个体或项目的全体——不一定指人，也不一定指一个国家。Sample（样本）指你实际收集数据的、总体的较小一部分，用来对总体作出估计。Census（普查）指从总体中每一个成员收集数据，完全不做抽样。
A census is completely accurate for the population but slow, expensive and often impossible; a sample is quicker and cheaper but only gives an estimate, so it can be wrong. Examiners frequently ask you to 'give one advantage and one disadvantage of using a sample rather than a census'.
普查对总体来说完全准确，但耗时长、成本高，常常无法实施；样本更快、更便宜，但只能给出估计，因此可能出错。考官经常问"使用样本而非普查的一个优点和一个缺点"。
| Term | 术语 | Meaning | 含义 |
| Population 总体 | Every item or individual being studied 被研究的全部个体 |
| Census 普查 | Data collected from every member of the population 从总体每个成员收集数据 |
| Sample 样本 | A subset of the population used for the study 总体中用于研究的一部分 |
| Sampling frame 抽样框 | A list of all members of the population 总体全体成员的名单 |
| Sampling unit 抽样单元 | Each individual item or person in the population 总体中的每一个个体 |
| Biased sample 有偏样本 | A sample that favours one part of the population 偏向总体某一部分的样本 |
Memory aid: picture a soup pot. The population is the whole pot of soup, the sample is one spoonful you taste, and a census would mean drinking the entire pot. That image never fails to fix the difference.
记忆辅助：想象一锅汤。总体是整锅汤，样本是你尝的一勺，普查则意味着把整锅都喝掉。这个画面能牢牢固定三者的区别。
5. Sampling Methods and Bias | 抽样方法与偏差
A simple random sample gives every member of the population an equal chance of being chosen. It is usually taken by numbering the whole population and using a random number generator, or by the lottery method of drawing names from a hat. It is the fairest basic method, but it can be slow and it may miss small sub-groups by pure chance.
简单随机抽样让总体中每个成员被选中的机会都相同。做法通常是把总体编号后使用随机数生成器，或者用"抽签法"从盒子里抽名字。它是最公平的基础方法，但可能较慢，而且纯凭运气也可能漏掉某些小群体。
A systematic sample takes every k-th item from an ordered list, where k equals the population size divided by the sample size. It is fast and easy to do, but it can be biased if the list has a repeating pattern, for example choosing every 10th house on a street where the houses are arranged in identical blocks.
系统抽样从有序名单中每隔 k 个取一个，其中 k ＝ 总体大小 ÷ 样本大小。它快速易行，但如果名单存在周期性规律就会产生偏差，例如在同一条街上每 10 户取一户，而房屋恰好按相同单元重复排列。
A stratified sample divides the population into groups (strata) that share a characteristic such as year group, gender or age, then takes a sample from each group in proportion to its size. It is the most representative method because every sub-group is guaranteed to appear, and it is very common in exam questions about school surveys.
分层抽样把总体按某一特征（如年级、性别、年龄）分成若干层，再按各层大小成比例地抽取。它是最有代表性的方法，因为每个子群体都必定被包含，在学校调查类考题中极为常见。
- Quota sampling: the interviewer is told to collect a fixed number from each group but chooses the people themselves. Fast, but not random and therefore biased.
配额抽样：访问员被要求从每组收集固定数量，但由他自己挑人。速度快，但不随机，因此有偏差。 - Opportunity (convenience) sampling: whoever is available at the time is used, for example asking the first 20 people in the canteen. Very biased.
偶遇（便利）抽样：谁在场就问谁，例如问食堂里最先遇到的 20 人。偏差很大。 - Bias: a systematic error that makes the sample unrepresentative of the population. A larger sample does not remove bias.
偏差：使样本无法代表总体的系统性误差。样本变大并不能消除偏差。
Typical exam wording: 'Give one reason why this sample may not be representative.' Strong answers name the missing group and the direction of the bias, for example 'only asking students in the library excludes those who rarely visit, and these students may read less'.
典型考法："说明为何该样本可能不具代表性。"高分答案要点出被遗漏的群体和偏差方向，例如"只问图书馆里的学生，会排除很少来图书馆的学生，而这些学生可能读书更少"。
6. Frequency Tables and Tally Charts | 频数表与画记图
Raw data is hard to read, so it is organised into a frequency table. A tally chart is the first stage: you record one vertical stroke per item and cross off every fifth stroke, then write the total in the frequency column. Frequency simply means how many times a value occurs.
原始数据难以阅读，所以要整理成频数表。画记图是第一步：每个项目画一竖笔，每第五笔划掉成组，然后把总数写进频数列。Frequency（频数）就是某个数值出现的次数。
is the size of the interval (here 10), and the midpoint is the average of the two ends (here 5, 15, and so on). Midpoints matter because you use them to estimate the mean of grouped data.
当数据是连续的，或取值很多时，要分组为组区间，如 0 ≤ x < 10、10 ≤ x < 20。组距（class width）是区间的宽度（这里是 10），组中值（midpoint）是两端点的平均（这里依次是 5、15……）。组中值很重要，因为估算分组数据的均值时要用到它。
| Term | 术语 | Meaning | 含义 |
| Tally 画记 | Stroke marks used to count items 用来计数的竖笔 |
| Frequency 频数 | The number of times a value occurs 数值出现的次数 |
| Class interval 组区间 | A group of values such as 10 ≤ x < 20 如 10 ≤ x < 20 这样的取值组 |
| Class width 组距 | The size of the interval 区间的宽度 |
| Midpoint 组中值 | The value in the middle of an interval 区间正中的值 |
| Cumulative frequency 累积频数 | A running total of frequencies 频数的逐个累加 |
| Relative frequency 相对频数 | Frequency divided by total frequency 频数除以总频数 |
Two-way tables (also called contingency tables) show two variables at once, for example year group down the side and preferred sport across the top. Always check the totals row and column: examiners often plant a deliberate slip to see whether you are reading the table carefully.
双向表（也称列联表）同时显示两个变量，例如侧边是年级、横排是喜欢的运动。一定要核对合计行与合计列：考官常会故意埋一个错误，看你是否仔细读表。
7. Measures of Average and Spread | 平均数与离散程度量
The three averages are the mean, the median and the mode. The mean is the total of all values divided by the number of values; the median is the middle value when the data is arranged in order; the mode is the value that occurs most often. For grouped data you cannot find a true median, so you name the modal class instead.
三种平均数是均值、中位数和众数。均值是所有数值之和除以数值个数；中位数是把数据排序后的中间值；众数是出现次数最多的值。对于分组数据，你无法求出真正的中位数，所以要说出众数组（modal class）。
mean = Σx ÷ n grouped mean = Σfx ÷ Σf
argest value − smallest value IQR = upper quartile − lower quartile
The range and the interquartile range (IQR) measure spread, also called dispersion. The range is quick but depends on just two values and is badly affected by an outlier. The IQR ignores the extreme quarters and is therefore more reliable when the data contains unusual values.
极差（range）与四分位距（IQR）衡量离散程度。极差算得快，但只依赖两个值，受异常值影响极大。IQR 忽略两端各四分之一的极端值，因此当数据含有异常值时更可靠。
- Mean: uses every value, works well for further calculation, but is pulled towards outliers.
均值：用到了每个数值，便于后续计算，但会被异常值拉偏。 - Median: not affected by outliers, good for skewed data, but ignores the actual size of most values.
中位数：不受异常值影响，适合偏斜数据，但忽略了大多数数值的实际大小。 - Mode: useful for qualitative data such as favourite colour, and for finding the most popular item, but a data set may have no mode or several modes.
众数：适用于定性数据（如最喜欢的颜色），可找出最受欢迎的项目，但一组数据可能没有众数，也可能有多个众数。 - e is that any value greater than UQ + 1.5 × IQR or less than LQ − 1.5 × IQR is an outlier.
异常值：与其余数据相距异常远的数值。常用规则是：大于 UQ + 1.5 × IQR 或小于 LQ − 1.5 × IQR 的值即为异常值。
Memory aid for quartiles: split the ordered data in half to find the median, then split each half in half again. The lower quartile is the median of the lower half, the upper quartile is the median of the upper half. If n is the number of values, the median sits at position (n + 1) ÷ 2.
四分位数的记忆口诀：先把有序数据对半分成上下两半找出中位数，再把每一半各对半分。下四分位数是下半部分的中位数，上四分位数是上半部分的中位数。若共有 n 个数值，中位数位于第 (n + 1) ÷ 2 个位置。
8. Presenting Data: Charts and Graphs | 数据呈现：统计图表
Choosing the right graph is a vocabulary question as much as a drawing question. Bar charts are for qualitative or discrete data and have gaps between the bars. Histograms are for continuous grouped data, have no gaps, and the area of each bar - not the height - represents the frequency, so you must label the vertical axis 'frequency density'.
选对图表既是画图题也是词汇题。条形图用于定性或离散数据，条形之间有间隔。直方图用于连续分组数据，条形之间没有间隔，每根条的面积（而不是高度）代表频数，因此纵轴必须标注为"频率密度"。
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