📚 IGCSE CAIE Statistics: Key Vocabulary Memory Guide | IGCSE CAIE 统计：词汇术语速记指南
In IGCSE CAIE Statistics, precise use of technical terms is often just as important as calculation. This memory guide groups the essential vocabulary into quick, exam-focused sections, with mnemonics, paired Chinese explanations, and simple Unicode formulas to help you recall definitions under time pressure.
在 IGCSE CAIE 统计中，准确使用术语往往和计算同样重要。本速记指南将核心词汇按考试重点分组，配以助记法、中英对照解释和简洁的 Unicode 公式，帮助你在时间紧张时快速回忆定义。
1. Core Statistical Terms: Population, Sample, Variable | 核心统计术语：总体、样本、变量
Population means the entire group you want to study. A sample is a smaller group selected from the population.
总体指你想研究的整个群体；样本是从总体中选出的一小部分。
Remember 'P' for population = whole picture; 'S' for sample = selected subset.
记忆：P 对应总体（整个画面），S 对应样本（选出的子集）。
A variable is any characteristic that can change or take different values, such as height or shoe size. Raw data are the original unprocessed observations collected before sorting or analysis.
变量是任何会变化或取不同值的特征，例如身高或鞋码。原始数据是在整理或分析之前收集的未经处理的观测值。
Quick memory: 'Population = all, sample = part, variable = what you measure.'
快速记忆：'总体是所有，样本是一部分，变量是你测量的内容。'
2. Types of Data: Qualitative vs Quantitative, Discrete vs Continuous | 数据类型：定性/定量、离散/连续
Qualitative data describes qualities or categories, like colour, gender or type of transport. Quantitative data records numerical measurements.
定性数据描述性质或类别，如颜色、性别或交通方式；定量数据记录数值度量。
Discrete data can only take exact, countable values, often integers: number of students, goals scored. Continuous data can take any value in an interval: height, time, mass.
离散数据只能取可数的精确值，通常是整数，如学生人数、进球数；连续数据可在区间内取任意值，如身高、时间、质量。
Mnemonic: 'D for dots' = discrete values are separate; 'C for connected' = continuous values flow along a scale.
助记：'D 代表点'——离散值彼此分开；'C 代表连续'——连续值沿刻度流动。
| Data type | Definition | Example |
|---|---|---|
| Qualitative | Categories or labels | Favourite colour |
| Quantitative discrete | Countable numerical values | Number of books |
| Quantitative continuous | Measurable numerical values | Height in cm |
Use this table to classify any variable quickly: first ask 'Is it a number?' If no, qualitative. If yes, then ask 'Can it be counted exactly?' If yes, discrete; if no, continuous.
用这个表格快速分类任何变量：首先问“它是数字吗？”如果不是，就是定性数据；如果是，再问“可以精确计数吗？”可以就是离散数据；不可以就是连续数据。
3. Measures of Central Tendency: Mean, Median, Mode | 集中趋势度量：平均数、中位数、众数
Mean is the arithmetic average. For raw data x₁, x₂, ..., xₙ, the mean is:
平均数是算术平均值。对于原始数据 x₁, x₂, ..., xₙ，平均数为：
x̄ = Σx ÷ n
Median is the middle value when data are arranged in order. For n values, the median position is (n + 1) ÷ 2.
中位数是将数据按顺序排列后的中间值。对于 n 个值，中位数位置为 (n + 1) ÷ 2。
Mode is the most frequent value. A data set can have one mode, more than one mode, or no mode at all if all values occur equally often.
众数是出现频率最高的值。一组数据可以有一个众数、多个众数，或者如果所有值出现次数相同则没有众数。
Quick recall: 'Mean = average, Median = middle, Mode = most'. In Chinese, 平均数求总和除以个数，中位数找中间，众数看最多。
快速记忆：'Mean 平均数、Median 中位数、Mode 众数'；中文可记“平均算总和、中位找中间、众数看最多”。
The mean uses every value and is affected by extreme values. The median is resistant to outliers. The mode is the only measure suitable for qualitative data.
平均数使用所有数值，并受极端值影响。中位数对离群值有抵抗力。众数是唯一适用于定性数据的集中趋势度量。
4. Measures of Spread: Range, Interquartile Range, Standard Deviation | 离散程度度量：极差、四分位距、标准差
Range is the simplest measure of spread: maximum value minus minimum value.
极差是最简单的离散程度度量：最大值减最小值。
The interquartile range (IQR) measures the spread of the middle 50% of data. It is Q₃ − Q₁, where Q₁ is the lower quartile and Q₃ is the upper quartile.
四分位距（IQR）度量中间 50% 数据的分散程度。IQR = Q₃ − Q₁，其中 Q₁ 是下四分位数，Q₃ 是上四分位数。
Standard deviation shows how far values typically deviate from the mean. The population standard deviation is:
标准差表示数值通常偏离平均数多远。总体标准差为：
σ = √(Σ(x − μ)² ÷ N)
Mnemonic for spreads: 'Range is one gap; IQR is the middle gap; SD is the typical gap from the centre.'
离散程度助记：'极差是两端距离；四分位距是中间距离；标准差是相对中心的典型距离。'
Larger spread means data are more varied. Smaller spread means data are more consistent. Exam questions often ask you to compare spreads using IQR or standard deviation, not range alone.
离散程度越大，数据变化越大；离散程度越小，数据越一致。考试题目常要求用四分位距或标准差来比较离散程度，而不是只用极差。
5. Frequency Distributions and Charts | 频数分布与图表
A frequency distribution lists values or groups with how often they occur. Class intervals must normally be equal for standard frequency charts, but histograms can use unequal widths.
频数分布列出数值或分组及其出现次数。标准频数图的组距通常应相等，但直方图可以使用不等组距。
Frequency density is used in histograms when class widths differ:
当组距不同时，直方图使用频率密度：
Frequency density = frequency ÷ class width
A bar chart is for categorical or discrete data with gaps between bars; a histogram is for continuous data with no gaps and area proportional to frequency.
条形图用于分类或离散数据，条形之间有间隔；直方图用于连续数据，条形无间隔，面积与频数成比例。
| Feature | Bar chart | Histogram |
|---|---|---|
| Data type | Categorical or discrete | Continuous |
| Gaps between bars | Yes | No |
广告 / Sponsored 【现货】剑桥国际高中教材 Cambridge IGCSE & O Level Additional Mathemati… 数学 备考教辅 · 正版现货 · 与本文内容相关 查看详情 / View on Taobao参考价 ¥198.0
更多咨询请联系16621398022（同微信） 备考资讯每日更新，关注不错过 考纲变化 · 科目分析 · 学习方法  在微信里长按二维码识别关注 或截图后用「扫一扫 → 相册」选择本图 公众号：tutorhao |