📚 Year 11 CIE Statistics: Vocabulary Flashcard Guide | 统计词汇术语速记指南
Statistical vocabulary can feel like a new language, but once you associate each term with a clear mental image or a simple story, recall becomes effortless. This guide breaks down the key CIE IGCSE Statistics terms into bite-sized paired explanations, helping you learn both the English terminology and its Chinese equivalent while building genuine understanding for exams.
统计学的词汇就像一门新语言，但一旦你能为每个术语配上清晰的画面或简单的故事，记忆就会变得毫不费力。本指南将 CIE IGCSE 统计的关键术语拆解成简短的中英对照解释，帮助你在学习英文术语和中文同时真正理解概念，自信应对考试。
1. Population and Sample | 总体与样本
A population is the complete set of individuals or items that you want to study. Think of it as the whole universe you care about, e.g. all students in Year 11 at your school. A sample is a smaller, manageable subset taken from that population, used to draw conclusions without testing every single member.
总体是你要研究的全部个体或项目的集合。可以把它想象成你关心的整个宇宙，例如学校所有 Year 11 学生。样本是从总体中抽取的一个较小且可处理的子集，用来推断结论而无需调查每一个成员。
- Census – data collected from every member of the population. / 普查 – 从总体中每一个成员收集的数据。
- Parameter – a numerical value describing a population. / 参数 – 描述总体的数值。
- Statistic – a numerical value calculated from a sample. / 统计量 – 由样本计算得出的数值。
2. Types of Data | 数据的类型
Data comes in different flavours. Quantitative data measure amounts (numbers), while qualitative data describe qualities (words or categories). Quantitative data can be discrete (counted values, e.g. number of cars) or continuous (measured values, e.g. height). Always check whether the data can take any value within a range before deciding.
数据有不同的面貌。定量数据测量数量（数字），而定性数据描述性质（词语或类别）。定量数据又可以分成离散型（可数的值，例如汽车辆数）或连续型（测量的值，例如身高）。在判断之前，首先确认数据是否可以在一个范围内取任意值。
- Primary data – collected by you for the specific investigation. / 一手数据 – 你为具体调查亲自收集的数据。
- Secondary data – data that has already been collected by someone else. / 二手数据 – 他人已经收集好的数据。
3. Measures of Central Tendency | 集中趋势的度量
The three musketeers of central tendency are mean, median and mode. The mean is the arithmetic average, sensitive to extreme values. The median is the middle value when data are ordered, resistant to outliers. The mode is the most frequent value. For a quick recall: 'Mean is unfair to extremes, Median is the middleman, Mode is the most popular.'
集中趋势的三剑客是平均数、中位数和众数。平均数是算术平均值，对极端值很敏感。中位数是排序后处于中间位置的值，不受异常值影响。众数是出现频率最高的值。快速记忆：“平均数怕极端，中位数坐中间，众数最爱露面。”
Mean = Σx ÷ n
- Σ (sigma) means 'sum of'. / Σ（西格玛）代表“总和”。
- n is the number of observations. / n 是观测值的个数。
4. Measures of Spread | 离散程度的度量
Central tendency alone is not enough; we need to know how spread out the data are. Range = max − min. Interquartile range (IQR) = Q₃ − Q₁, the middle 50% of data. Variance is the average of squared deviations from the mean, and standard deviation is its positive square root. Imagine the standard deviation as the typical distance from the centre.
仅有集中趋势还不够，我们还需要知道数据的分散程度。极差 = 最大值 − 最小值。四分位距 (IQR) = Q₃ − Q₁，涵盖中间 50% 的数据。方差是每个值与平均数之差的平方的平均数，标准差是它的正平方根。可以把标准差想象成数据点离中心的“典型距离”。
Variance = Σ(x − x̄)² ÷ n
- Quartile: Q₁ is lower quartile (25th percentile), Q₂ is median, Q₃ is upper quartile. / 四分位数：Q₁ 下四分位数（第25百分位），Q₂ 中位数，Q₃ 上四分位数。
5. Probability Fundamentals | 概率基础
Probability measures chance between 0 (impossible) and 1 (certain). An experiment is a repeatable process with defined outcomes. The sample space is the set of all possible outcomes. An event total outcomes). Think of sample space as a complete menu, and event as the dish you order.
概率衡量的是 0（不可能）到 1（必然）之间的可能性。试验是一个可重复且有确定结果的过程。样本空间是所有可能结果的集合。事件是样本空间的一个子集。在等可能结果的情况下，概率 = （有利结果数）/（所有结果数）。把样本空间想象成一份完整的菜单，事件就是你点的那道菜。
- Mutually exclusive events cannot happen at the same time. / 互斥事件不可能同时发生。
- Independent events: occurrence of one does not affect the probability of the other. / 独立事件：一个事件的发生不影响另一个事件的概率。
6. Random Variables and Expectation | 随机变量与期望
A random variable (X) assigns a number to each outcome of an experiment. The probability distribution lists the values X can take and their probabilities. The expected value E(X) is the long-run average: multiply each value by its probability and sum them. Think of expected value as what you’d get on average if you repeated the experiment forever.
随机变量 (X) 为试验的每个结果分配一个数值。概率分布列出了 X 可能取的值及其概率。期望值 E(X) 是长期平均值：每个值乘以其概率后再求和。将期望值想象成如果你无数次重复该试验，平均每次能得到的结果。
E(X) = Σ [x × P(X=x)]
- Discrete random variable takes distinct values. / 离散型随机变量取值为分开的个别值。
7. Sampling Methods | 抽样方法
How you choose a sample affects the quality of your conclusions. Random sampling gives every member an equal chance; use a random number generator. Stratified sampling divides the population into layers (strata) and picks randomly from each in proportion to size. Systematic sampling selects every kth item. Bias creeps in when the sample does not fairly represent the population – avoid convenience sampling!
选择样本的方式直接影响结论的质量。随机抽样给每个成员同等的被选机会；使用随机数生成器。分层抽样先将总体划分为层，再从每一层按比例随机抽取。系统抽样每隔 k 个选一个样本。偏差会在样本不能公平代表总体时偷偷溜进来 —— 避免便利抽样！
- Quota sampling – interviewer fills quotas within categories; non-random. / 配额抽样 – 访问员按类别填充配额，非随机。
- Capture-recapture – used to estimate population size (e.g. animals). / 捕获-再捕获 – 用于估计种群数量（如动物）。
8. Graphs and Charts | 图表类型
Visuals tell stories quickly. A bar chart compares categories with gaps between bars; a histogram shows frequency density for continuous grouped data (no gaps). A pie chart displays proportions of a whole. A cumulative frequency graph leads to a smooth S-shape for estimating medians and quartiles. A box-and-whisker plot summarises five key numbers: min, Q₁, median, Q₃, max.
图表能迅速讲述数据的故事。条形图用条形间的空隙来比较类别；直方图用频率密度展示连续分组数据（无空隙）。饼图显示各部分占整体的比例。累积频数图生成平滑的 S 形曲线，用于估算中位数和四分位数。箱线图概括了五个关键数字：最小值、下四分位数、中位数、上四分位数、最大值。
- Scatter diagram – shows relationship between two variables. / 散点图 – 展示两个变量之间的关系。
- Line of best fit – a straight line drawn through scatter points that best represents the trend. / 最佳拟合线 – 穿过散点的直线，最能代表趋势。
9. Correlation and Regression | 相关与回归
Correlation measures the strength and direction of a linear relationship between two variables. Positive correlation: as one increases, the other tends to increase. Negative correlation: as one increases, the other tends to fall. Zero correlation means no linear pattern. Causation is a stronger claim — other. Regression gives a formula for the line of best fit, often in the form y = mx + c.
相关衡量两个变量之间线性关系的强度和方向。正相关：一个增加，另一个也倾向于增加。负相关：一个增加，另一个倾向于减少。零相关意味着不存在线性模式。因果关系是一个更强烈的主张 —— 两件事一起变动并不代表一个导致了另一个。回归给出最佳拟合线的公式，通常形式为 y = mx + c。
- Correlation coefficient (r) – ranges from −1 (perfect negative) to +1 (perfect positive). / 相关系数 r – 范围从−1（完全负相关）到 +1（完全正相关）。
- Interpolation – predicting inside the data range; extrapolation – predicting beyond, riskier. / 内插 – 在数据范围内预测；外推 – 在数据范围外预测，风险更高。
10. Distributions and Shapes | 分布与形状
The normal distribution is the famous bell-shaped curve, symmetric and centred on the mean. Most data cluster around the middle. A skew occurs when a distribution is lopsided: positive skew has a tail to the right, negative skew a tail to the left. In a positively skewed distribution, mean > median > mode; the opposite for negative skew. Use a memory trick: 'Mean chases the tail.'
正态分布是著名的钟形曲线，对称且以平均值为中心，大多数数据聚集在中部。偏斜发生在分布不对称时：正偏斜的尾部向右，负偏斜的尾部向左。在正偏斜分布中，平均值 > 中位数 > 众数；负偏斜则相反。记忆技巧：“平均数追着尾巴跑。”
- Uniform distribution – all outcomes equally likely, flat shape. / 均匀分布 – 所有结果等可能，形状平坦。
- Bimodal – distribution with two peaks. / 双峰 – 有两个峰的分布。
11. Hypothesis Testing Basics | 假设检验基础
In CIE exams, you may encounter the logic of testing claims. A null hypothesis (H₀) is the default statement (e.g. 'the coin is fair'). An alternative hypothesis (H₁) is what you suspect. You compare an observed result to what is expected under H₀. If the result is very unlikely (low p-value), you reject H₀. The significance level is the threshold for deciding 'unlikely', often 5%.
在 CIE 考试中，你可能会遇到检验观点的主线逻辑。零假设 (H₀) 是默认陈述（如“硬币是公平的”）。备择假设 (H₁) 是你怀疑的猜测。你将观察到的结果与在 H₀ 下的期望进行比较。如果结果非常不可能发生（p 值很小），你便拒绝 H₀。显著性水平是决定“不可能”的门槛，通常为 5%。
- One-tailed test – investigates an effect in one direction. / 单尾检验 – 检验单一方向的效果。
- Two-tailed test – investigates any difference, both sides. / 双尾检验 – 检验任何差异，左右两侧都考虑。
12. Quick Memory Hacks | 快速记忆技巧
Build mental bridges for statistics vocabulary. For 'discrete vs continuous', think: discrete = 'distinct dots' (countable things); continuous = 'connected curve' (measurements). For 'parameter vs statistic', remember: Population → Parameter; Sample → Statistic. For the mean/median/mode order in skewness, chant: 'Mo, Me, Mea' – mode stays where most data are, median nearer the centre, mean pulled toward the tail. Flashcards with these images will accelerate your revision.
为统计词汇搭建思维桥梁。对于“离散与连续”，想象：离散 = “分明的点”（可数事物）；连续 = “相连的曲线”（测量值）。对于“参数与统计量”，记住：Population → Parameter；Sample → Statistic。对于偏斜分布中平均数、中位数和众数的顺序，可以默念：“众、中、均” —— 众数守着数据最多的地方，中位数更接近中心，平均数被拉向尾巴。把这些图像放进记忆卡片，复习效率会大大提高。
| Trick / 窍门 | Remember / 记忆点 |
|---|---|
| IQR = Q₃ − Q₁ | '3 take away 1' — the middle 50% range. / 用 3 减 1 得到中间 50% 的范围。 |
| Outlier limits | Q₁ − 1.5×IQR and Q₃ + 1.5×IQR — 'fence posts' for extreme values. / 把 1.5 倍 IQR 当作异常值的“栅栏”。 |
| Scatter slope sign | Up to the right = positive; Down to the right = negative. / 向右上方走为正相关，向右下方走为负相关。 |
Published by TutorHao | Statistics Revision Series | aleveler.com
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