📚 OCR Statistics Vocabulary Quick-Memorisation Guide | OCR 统计词汇术语速记指南
Mastering the language of statistics is half the battle in Year 11 OCR exams. This guide pairs every key term with a simple memory hook, so you can recall definitions fast and apply them accurately in data-handling, probability, and statistical-inference questions.
掌握统计学的语言，是应对 Year 11 OCR 考试成功的一半。本指南为每个关键术语搭配了简单的记忆挂钩，帮助你快速回忆定义，并在数据处理、概率和统计推断题中准确应用。
1. Population, Sample, Census | 总体、样本、普查
A population is the entire group of individuals or items you want information about. Think ‘P’ for ‘Pool of everyone’. A sample is a subset of the population selected for study. A census collects data from every member of the population. Census = Complete count.
总体 (population) 是你想要了解的全部个体或项目。记作“所有人的池子”。样本 (sample) 是从总体中选出的一个子集。普查 (census) 则收集总体中每个成员的数据。Census = 全面计数。
- Population: all GCSE students in England.
- 总体：英格兰所有 GCSE 学生。
- Sample: 200 randomly chosen GCSE students from 5 schools.
- 样本：从 5 所学校随机抽取的 200 名 GCSE 学生。
Memory hook: Census sounds like ‘sense us’ — it makes sense of all of us by asking everyone.
记忆挂钩：Census 听起来像“全面审视我们”——它通过询问每个人来了解我们全体。
2. Sampling Frame and Bias | 抽样框与偏差
A sampling frame is a list of all members of the population from which the sample is drawn. If the frame is incomplete, some groups may be excluded, leading to bias. Bias is a systematic error that distorts results in one direction.
抽样框 (sampling frame) 是总体中所有成员的列表，样本从此列表中抽取。如果抽样框不完整，某些群体可能被排除，从而产生偏差 (bias)。偏差是一种使结果朝一个方向扭曲的系统性误差。
Example: Using a telephone directory as a sampling frame misses people without landlines — introduces bias.
示例：使用电话簿作为抽样框会遗漏没有固定电话的人——引入偏差。
Memory hook: ‘Frame’ like a picture frame — if the frame cuts part of the picture, your view is biased.
记忆挂钩：“Frame”像画框——如果画框裁掉了画面的一部分，你的视野就有偏差。
3. Types of Data: Qualitative vs. Quantitative | 数据类型：定性数据与定量数据
Qualitative data is non-numerical and describes qualities or categories (e.g. eye colour, car brand). Quantitative data is numerical and can be counted or measured. Quantitative splits further into discrete (countable, like number of siblings) and continuous (measurable, like height).
定性数据 (qualitative data) 是非数值的，描述性质或类别（如眼睛颜色、汽车品牌）。定量数据 (quantitative data) 是数值的，可以计数或测量。定量数据又分为离散型 (discrete)（可数，如兄弟姐妹个数）和连续型 (continuous)（可测，如身高）。
- Qualitative: favourite subject — Art, Maths, Music.
- 定性：最喜欢的科目——美术、数学、音乐。
- Quantitative discrete: number of pets — 0, 1, 2, …
- 定量离散：宠物数量——0、1、2、……
- Quantitative continuous: mass of a potato — 150.3 g.
- 定量连续：一个土豆的质量——150.3 克。
Memory hook: ‘Quant’ rhymes with ‘count’ — quantitative is about numbers.
记忆挂钩：“Quant”与“count”押韵——定量数据与数字有关。
4. Primary and Secondary Data | 一手数据与二手数据
Primary data is collected directly by the researcher for a specific purpose (e.g. your own survey). Secondary data is data that already exists, collected by someone else (e.g. census data, internet databases). Primary = fresh and specific; Secondary = used, may be cheaper but less tailored.
一手数据 (primary data) 是研究者为特定目的直接收集的数据（如你自己做的调查）。二手数据 (secondary data) 是已经存在、由他人收集的数据（如普查数据、互联网数据库）。一手数据新鲜且针对性强；二手数据是现成的，可能更便宜但贴合度较低。
Memory hook: Primary is ‘prime’ — you are the first to collect it.
记忆挂钩：Primary 像“prime（首要）”——你是第一个收集它的人。
5. Mean, Median, Mode | 平均数、中位数、众数
The mean (x̄) is the sum of all values divided by the count: Σx / n. The median is the middle value when data is ordered. The mode is the most frequent value. Mean uses all data but is affected by outliers; median is robust to outliers; mode is the only measure suitable for qualitative data.
平均数 (mean, 念 x-bar) 是所有值的总和除以个数：Σx / n。中位数 (median) 是数据按顺序排列后的中间值。众数 (mode) 是出现频率最高的值。平均数用了所有数据但受异常值影响；中位数对异常值稳健；众数是唯一适合定性数据的集中量数。
- Data: 2, 3, 3, 5, 7 → mean = 20/5 = 4; median = 3; mode = 3.
- 数据：2, 3, 3, 5, 7 → 平均数 = 20/5 = 4；中位数 = 3；众数 = 3。
Memory hook: ‘Median’ — think ‘middle of the road’. ‘Mode’ sounds like ‘most’.
记忆挂钩：“Median”——“路中间”，中位数。“Mode”听起来像“most（最多）”。
6. Range and Interquartile Range (IQR) | 极差与四分位距
The range is the difference between the largest and smallest values. The interquartile range (IQR) is the difference between the upper quartile (Q3) and lower quartile (Q1). IQR measures the spread of the middle 50% and is not affected by extreme values.
极差 (range) 是最大值与最小值的差。四分位距 (IQR) 是上四分位数 (Q3) 与下四分位数 (Q1) 的差。IQR 衡量中间 50% 数据的离散程度，不受极端值影响。
IQR = Q3 − Q1. Outliers are often defined as values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR.
IQR = Q3 − Q1。异常值常定义为低于 Q1 − 1.5×IQR 或高于 Q3 + 1.5×IQR 的值。
Memory hook: ‘Interquartile’ — imagine the middle two quarters of an orange, the rest is trimmed.
记忆挂钩：“Interquartile”——想象一个橙子的中间两瓣，其余的被削掉了。
7. Standard Deviation and Variance | 标准差与方差
Variance is the average of the squared differences from the mean. Standard deviation (σ or s) is the square root of the variance. It shows how much, on average, each data point deviates from the mean. A small SD means data is tightly clustered; a large SD means widespread values.
方差 (variance) 是各数据与平均数之差的平方的平均值。标准差 (standard deviation, σ 或 s) 是方差的平方根。它反映了每个数据点平均偏离平均数的程度。标准差小表示数据集中；标准差大表示数据分散。
Formula for sample standard deviation: s = √[ Σ(x − x̄)² / (n−1) ]
样本标准差公式：s = √[ Σ(x − x̄)² / (n−1) ]
Memory hook: ‘Deviation’ = how much you deviate from the ‘standard’ average.
记忆挂钩：“Deviation” = 你偏离“标准”平均数的程度。
8. Probability: Experiment, Outcome, Event, Sample Space | 概率：试验、结果、事件、样本空间
An experiment is a repeatable process with a set of possible results. An outcome is a single possible result. An event is a set of one or more outcomes. The sample space is the list of all possible outcomes. Probability of an event = number of favourable outcomes / total number of outcomes.
试验 (experiment) 是一个可重复的过程，有一组可能的结果。结果 (outcome) 是单个可能的结果。事件 (event) 是由一个或多个结果组成的集合。样本空间 (sample space) 是所有可能结果的列表。事件的概率 = 有利结果数 / 总结果数。
- Experiment: rolling a fair six-sided die.
- 试验：掷一枚均匀的六面骰子。
- Sample space: {1, 2, 3, 4, 5, 6}.
- 样本空间：{1, 2, 3, 4, 5, 6}。
- Event ‘even number’: {2, 4, 6}; probability = 3/6 = ½.
- 事件“偶数”：{2, 4, 6}；概率 = 3/6 = ½。
Memory hook: Sample space is like a restaurant menu — it lists everything you could possibly order.
记忆挂钩：样本空间就像餐厅菜单——列出了你可能点到的所有东西。
9. Relative Frequency and Expected Frequency | 相对频率与期望频数
Relative frequency is an estimate of probability based on data from an experiment: number of times an event occurs ÷ total number of trials. Expected frequency is the number of times you expect an event to occur in a certain number of trials: probability × number of trials.
相对频率 (relative frequency) 是基于实验数据对概率的估计：事件发生次数 ÷ 试验总次数。期望频数 (expected frequency) 是在一定试验次数中预期事件发生的次数：概率 × 试验次数。
If a die is rolled 300 times, expected frequency of a ‘4’ = (1/6) × 300 = 50.
若掷骰子 300 次，“4”的期望频数 = (1/6) × 300 = 50。
Memory hook: Relative frequency — ‘relative’ to the total trials, not absolute.
记忆挂钩：Relative frequency——“相对”于总试验次数，不是绝对次数。
10. Scatter Graphs, Correlation and Line of Best Fit | 散点图、相关性与最佳拟合线
A scatter graph shows the relationship between two variables. Correlation describes the direction and strength of that relationship: positive (as one increases, the other increases), negative (one increases, other decreases), or none. The correlation coefficient (r) ranges from −1 (perfect negative) to +1 (perfect positive). A line of best fit can be drawn to model the trend and make predictions.
散点图 (scatter graph) 显示两个变量之间的关系。相关性 (correlation) 描述这种关系的方向和强度：正相关 (positive)（一个增加，另一个也增加）、负相关 (negative)（一个增加，另一个减少）或无相关。相关系数 (r) 的范围从 −1（完全负相关）到 +1（完全正相关）。可以画一条最佳拟合线 (line of best fit) 来模拟趋势并进行预测。
Memory hook: Correlation is not causation — just because two things move together doesn’t mean one causes the other.
记忆挂钩：相关性不代表因果关系——两个事物同时变化并不意味着一个导致了另一个。
11. Cumulative Frequency and Box Plots | 累积频率与箱线图
Cumulative frequency is the running total of frequencies. A cumulative frequency graph can be used to find quartiles and the median. A box plot (box-and-whisker diagram) displays the minimum, Q1, median, Q3, and maximum. It is a visual summary of spread and skewness.
累积频率 (cumulative frequency) 是频率的累计总和。累积频率图可用于查找四分位数和中位数。箱线图 (box plot) 显示最小值、Q1、中位数、Q3 和最大值。它是数据离散程度和偏态的直观总结。
Memory hook: Cumulative frequency — ‘accumulate’ as you go; Box plot — think of a box holding the middle 50% of data.
记忆挂钩：Cumulative frequency——“逐步累加”；Box plot——想象一个盒子装住了中间 50% 的数据。
12. Histograms and Frequency Density | 直方图与频率密度
A histogram is a diagram for grouped continuous data. Unlike a bar chart, the area of each bar represents frequency. If class widths are unequal, you must use frequency density = frequency ÷ class width. Bar height = frequency density.
直方图 (histogram) 是用于分组连续数据的图表。与条形图不同，每个柱形的面积代表频率。如果组距不等，必须使用频率密度 (frequency density) = 频率 ÷ 组距。柱高 = 频率密度。
Memory hook: Histogram bars touch each other; bar chart bars don’t. Frequency density — ‘density’ = frequency per unit width, like population density.
记忆挂钩：直方图的柱子紧挨着；条形图的柱子分开。Frequency density——“密度” = 每单位宽度的频率，就像人口密度。
Published by TutorHao | Statistics Revision Series | aleveler.com
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