📚 Year 11 OCR Sociology: Key Formulae and Theorems Quick Reference | OCR 社会学公式定理速查手册
Welcome to your quick-reference handbook for Year 11 OCR Sociology. This guide distils essential statistical formulae used in research methods and presents core sociological theories as formal 'theorems' rooted in the work of key thinkers. Each entry pairs a concise English explanation with its Chinese equivalent, so you can grasp and recall the material efficiently. Whether you are revising for a mock or the final GCSE, keep this collection to hand.
欢迎使用这本 Year 11 OCR 社会学速查手册。本手册浓缩了研究方法中必不可少的统计公式，并将核心社会学理论以关键思想家提出的正式“定理”形式呈现。每个条目都配有简洁的英文说明与中文对照，帮助你高效理解和记忆。无论你是在为模拟考试还是最终的普通中等教育证书考试复习，都请将此手册收好。
1. Mean, Median, Mode & Range – Descriptive Statistics | 平均数、中位数、众数和极差——描述性统计
Descriptive statistics summarise numerical data in social research. The mean is the arithmetic average, calculated by adding all values and dividing by the total number of cases. The median is the middle value when data are ordered. The mode is the most frequently occurring value. The range shows spread by subtracting the smallest value from the largest.
描述性统计概括社会研究中的数值数据。平均数是算术平均值，计算方式为所有数值相加后除以个案总数。中位数是将数据排序后位于中间的值。众数是出现频率最高的值。极差通过最大值减去最小值来显示数据的分散程度。
Mean (x̄) = Σx ÷ n
Range = Xₘₐₓ − Xₘᵢₙ
If family incomes are £20k, £25k, £30k, £55k, the mean is £32.5k but the median (£27.5k) is less distorted by the high earner.
若家庭收入为2万、2.5万、3万、5.5万英镑，平均数为3.25万英镑，但中位数（2.75万英镑）较少受高收入者的扭曲。
The mode helps identify the most common attitude in a Likert-scale survey.
众数有助于确定李克特量表调查中最常见的态度。
2. Percentage Change & Rate Calculations – Analytical Tools | 百分比变化和比率计算——分析工具
Sociologists often measure change over time or compare groups using percentages and rates. A percentage change reveals relative growth or decline. A rate per 1,000 (e.g. crime rate, birth rate) standardises comparisons across populations of different sizes.
社会学家常使用百分比和比率来测量随时间发生的变化或比较不同群体。百分比变化揭示相对的增长或下降。每千人的比率（例如犯罪率、出生率）可对规模不同的人口进行标准化比较。
Percentage Change = (New Value − Original Value) ÷ Original Value × 100%
Rate per 1,000 = (Number of Events ÷ Population at Risk) × 1,000
If GCSE pass rates rise from 65% to 72%, this is a +10.8% change.
若普通中等教育证书通过率从65%上升到72%，变化幅度为+10.8%。
A crime rate of 85 per 1,000 means 85 recorded crimes for every 1,000 residents.
犯罪率为85/千人意味着每千名居民中有85起被记录的犯罪案件。
3. Functionalism: The Organic Analogy Theorem | 功能主义：有机体类比定理
Functionalism, shaped by Emile Durkheim and Talcott Parsons, views society as a system of interdependent parts (institutions) that work together like a biological organism. Stability is maintained through value consensus and socialisation. Each institution fulfils a function: the family provides primary socialisation, education sifts and selects, and religion reinforces collective conscience.
功能主义由埃米尔·涂尔干和塔尔科特·帕森斯等人塑造，将社会视为一个由相互依赖的部分（制度）组成的系统，它们像生物有机体一样协同运作。社会稳定通过价值共识和社会化得以维持。每个制度都履行某种功能：家庭提供初级社会化，教育进行分等和选拔，宗教则强化集体良知。
Theorem: Social stability = f(value consensus, integration of institutions)
Durkheim’s study of suicide showed that too little or too much integration raises suicide rates – a functionalist proof of the need for balance.
涂尔干对自杀的研究表明，整合过弱或过强都会提高自杀率，这从功能主义角度证明了平衡的必要性。
Parsons’ AGIL schema formalises the four functional prerequisites: Adaptation, Goal attainment, Integration, Latency.
帕森斯的 AGIL 图式将四个功能先决条件正式化为：适应、目标达成、整合与模式维持。
4. Marxism: Base–Superstructure Theorem | 马克思主义：基础–上层建筑定理
Karl Marx’s theorem states that the economic base (relations of production, e.g. bourgeoisie vs. proletariat) shapes the superstructure (family, education, media, religion, law). The superstructure legitimises ruling‑class power and reproduces class inequality. Revolution is predicted when the contradictions of capitalism become too sharp.
卡尔·马克思的定理指出，经济基础（生产关系，如资产阶级与无产阶级的对立）决定上层建筑（家庭、教育、媒体、宗教、法律）。上层建筑使统治阶级的权力合法化，并再产生阶级不平等。当资本主义的矛盾变得过于尖锐时，革命就将到来。
Theorem: Superstructure ∼ f(Base); false consciousness masks exploitation.
Bowles and Gintis applied this to education: the hidden curriculum prepares working‑class pupils for docile labour, mirroring the capitalist workplace.
鲍尔斯与金蒂斯将此应用于教育：隐性课程将工人阶级学生培养成温顺的劳动者，与资本主义工作场所如出一辙。
Althusser distinguished between Repressive State Apparatuses (police, army) and Ideological State Apparatuses (media, religion) that maintain the base.
阿尔都塞区分了维护基础的镇压性国家机器（警察、军队）与意识形态国家机器（媒体、宗教）。
5. Feminism: Patriarchy Theorem | 女性主义：父权制定理
Feminist sociology asserts that society is structured by patriarchy – a system of male dominance that operates in all spheres. This ‘theorem’ predicts that gender inequality is not natural but socially constructed and reproduced through gendered socialisation, the division of labour, and institutional discrimination.
女性主义社会学主张，社会是由父权制——一种在一切领域中运作的男性支配体系——构成的。这一“定理”预测，性别不平等并非自然形成，而是由社会建构并通过性别社会化、劳动分工和制度性歧视再产生的。
Theorem: Gender stratification = patriarchy × institutional reinforcement.
Liberal feminists like Oakley demonstrated how canalisation and manipulation steer boys and girls into unequal roles from infancy.
像奥克利这样的自由主义女性主义者展示了如何通过引导和操纵从婴儿期便将男孩和女孩推向不平等的角色。
Radical feminists (e.g. Firestone) see the patriarchal family as the root of all oppression; Delphy and Leonard argue that women form a ‘sex class’ exploited through domestic labour.
激进女性主义者（如费尔斯通）将父权家庭视为一切压迫的根源；德尔菲与伦纳德则认为妇女构成了一个通过家务劳动被剥削的“性阶级”。
6. Interactionism: Labelling Theorem | 互动论：标签定理
Drawing on Mead’s symbolic interactionism, the labelling theorem holds that deviance and identity are shaped by social reaction rather than inherent qualities. Becker famously stated: ‘Deviance is not a quality of the act a person commits, but rather a consequence of the application by others of rules and sanctions.’ A master status can override all other identities.
标签定理借鉴米德的符号互动论，认为偏差与身份是由社会反应而非内在特质塑造的。贝克尔有一句名言：“偏差并非个人行为本身的属性，而是他人应用规则与制裁的后果。”一个主要身份可能凌驾于所有其他身份之上。
Theorem: Self-fulfilling prophecy = label + societal reaction.
Rosenthal and Jacobson’s ‘Pygmalion in the Classroom’ showed that when teachers were told certain pupils were ‘spurters’, those pupils’ IQ scores rose – a self‑fulfilling prophecy.
罗森塔尔与雅各布森的《课堂上的皮格马利翁》表明，当教师被告知某些学生是“将要冒升的”时，那些学生的智商分数真的上升了——这就是自我实现的预言。
In crime, Lemert distinguished primary deviance (the initial act) from secondary deviance (the outcome of being labelled), explaining how labelling amplifies delinquency.
在犯罪学中，莱默特区分了初级偏差（初始行为）与次级偏差（被贴标签后的结果），解释了标签如何放大失范行为。
7. Durkheim’s Anomie Theorem of Crime | 涂尔干的失范犯罪定理
Durkheim’s theorem posits that crime is a normal and inevitable feature of all societies, performing boundary‑maintenance and adaptive functions. However, rapid social change can produce anomie – a state of normlessness where the collective conscience weakens, deregulating human desires and raising crime rates.
涂尔干的定理认为，犯罪是所有社会中正常且不可避免的特征，发挥着维持边界和促进适应的功能。然而，急剧的社会变迁会导致失范——一种集体良知弱化、社会规范缺失的状态，使人欲失去调控，从而推高犯罪率。
Anomie = f(social change, deregulation of moral norms).
Durkheim used the shift from mechanical to organic solidarity to explain why industrialising societies experience temporary anomie.
涂尔干用机械团结向有机团结的转变，解释了为什么工业化社会会出现暂时的失范。
Merton later adapted this into Strain Theory, where anomie results from a gap between cultural goals and the legitimate means to achieve them.
默顿后来将其发展为压力理论，即失范源于文化目标与达到这些目标的合法手段之间的脱节。
8. Weber’s Theorem of Stratification | 韦伯的分层定理
Max Weber challenged Marx’s purely economic model by proposing a multidimensional theorem of stratification. Social inequality is shaped not only by class (market position, life chances) but also by status (social honour, lifestyle) and party (political power). These three dimensions can intersect and conflict.
马克斯·韦伯挑战了马克思的纯经济模型，提出了一个多维分层定理。社会不平等不仅由阶级（市场处境、生活机会）决定，还受地位（社会荣誉、生活方式）和党派（政治权力）的影响。这三个维度可能相互交叉，也可能彼此冲突。
Stratification = Class × Status × Party.
An impoverished aristocrat may have high status but low class, illustrating the independence of dimensions.
一位没落贵族可能地位很高但阶级很低，这说明了各维度之间的独立性。
Weber’s notion of ‘social closure’ – groups restricting access to resources – explains how professions like medicine maintain privilege through credentialism.
韦伯的“社会封闭”概念——群体限制资源准入——解释了医学等职业如何通过文凭主义维持特权。
9. The Relative Deprivation Formula (Social Inequality) | 相对剥夺公式（社会不平等）
Relative deprivation, developed by Runciman, is a measure of subjective inequality. Individuals feel deprived not when they lack resources in absolute terms, but when they compare themselves to a reference group and perceive a gap. The formula specifies conditions for this feeling to arise.
相对剥夺概念由朗西曼提出，是一种主观不平等度量。人们感到被剥夺并非因为资源绝对匮乏，而是因为他们将自己与参照群体进行比较，并感知到差距。公式具体说明了这种感觉产生的条件。
Relative Deprivation occurs when: A wants X, sees B has X, believes it is feasible to obtain X, yet lacks X – and feels this is unjust.
Townsend’s research on poverty in the UK used a deprivation index (including items like having a cooked breakfast or a holiday) to measure relative poverty.
汤森对英国贫困的研究使用了剥夺指数（包含如能吃上做好的早餐或度一次假等项目）来测量相对贫困。
The concept explains why crime may rise even in an affluent society: expectations grow faster than means.
这一概念解释了为何富裕社会中犯罪率仍可能上升：期望的增长快于手段的增长。
10. Social Mobility Rate – Intergenerational Formula | 社会流动率——代际公式
Sociologists quantify social mobility by comparing occupational positions across generations. The absolute mobility rate counts the proportion of individuals who end up in a different class from their parents. The relative mobility rate (odds ratio) shows the chances of moving up or down compared with those born into a different class.
社会学家通过比较代际职业位置来量化社会流动。绝对流动率计算最终进入与父母不同阶级的个人所占比例。相对流动率（比值比）则显示与其他阶级出身者相比，向上或向下流动的几率。
Absolute Mobility Rate = (Number mobile ÷ Total sample) × 100%
Relative Mobility (odds ratio) = (P₁ / (1−P₁)) ÷ (P₂ / (1−P₂)), where P₁ and P₂ are the chances of moving up for different starting classes.
The Oxford Mobility Study (Goldthorpe et al.) found high absolute mobility in post‑war Britain but limited relative mobility – the ‘long‑range’ mobility gap persisted.
牛津流动研究（戈德索普等人）发现战后英国绝对流动率很高，但相对流动率有限——“长距离”流动的差距依然存在。
Calculating odds ratios helps demonstrate that class of origin remains a powerful predictor of destination.
计算比值比有助于证明出身阶级仍然是预测最终阶级的有力因素。
11. The ‘Dark Figure’ of Crime Theorem | 犯罪黑数定理
Official crime statistics never capture the full extent of offending. The dark figure – unrecorded, unreported, or undiscovered crime – is a central theorem in the sociology of crime and deviance. It arises from factors such as victim reluctance to report, police recording practices, and the invisibility of certain offences like corporate crime.
官方犯罪统计数据永远无法反映犯罪的全貌。黑数——未被记录、未被报告或未被发现的犯罪——是犯罪与偏差社会学中的一个核心定理。其产生原因包括受害者不愿报案、警方的记录惯例，以及公司犯罪等特定罪行难以被发现。
Dark Figure = Real Crime Level − Officially Recorded Crime.
The Crime Survey for England and Wales (CSEW) routinely uncovers higher victimisation rates than police figures, especially for domestic abuse and sexual offences.
英格兰和威尔士犯罪调查通常揭示出的受害率高于警方数据，尤其在家暴和性犯罪方面。
Feminist sociologists argue that patriarchal structures contribute to the dark figure by silencing victims of gender‑based violence.
女性主义社会学家认为，父权结构通过压制性别暴力受害者的发声，助长了黑数的存在。
12. Sampling: Probability and Non-Probability Formulae | 抽样：概率与非概率公式
Generalisable research requires a representative sample. Probability sampling uses random selection; the sampling fraction formula ensures proportionality. In non‑probability sampling (quota, snowball), researchers use purposive criteria. Understanding these calculations helps evaluate OCR research methods questions on reliability and representativeness.
可推广的研究需要一个有代表性的样本。概率抽样采用随机选择；抽样分数公式确保比例合理。在非概率抽样（定额、滚雪球）中，研究者使用目的性标准。理解这些计算有助于你在 OCR 研究方法题中评估信度和代表性。
Sampling Fraction = Sample Size (n) ÷ Population Size (N)
If strata are used, nₛₜᵣₐₜₐ = (Nₛₜᵣₐₜₐ ÷ N) × n
A sample of 200 from a population of 10,000 pupils gives a sampling fraction of 0.02 (2%).
从10,000名学生中抽取200个样本，抽样分数为0.02（2%）。
Snowball sampling starts with one respondent who refers others; it is useful for hidden populations, but the sampling fraction is not controlled, making statistical generalisation impossible.
滚雪球抽样从一个受访者开始，由其介绍他人；此方法对隐藏群体很有效，但抽样分数不受控制，因而无法进行统计推广。
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