📚 Year 11 Eduqas Sociology: Formulas and Theorems Quick Reference | 社会学公式定理速查手册
This revision handbook brings together the essential quantitative formulas and the core theoretical 'theorems' you need for the Eduqas GCSE Sociology exam. It covers research-method calculations that appear in data-response questions, alongside the key propositions from functionalism, Marxism, feminism, interactionism and Weberian sociology. Use it as a rapid check before your test, making sure you can apply both the numbers and the big ideas with confidence.
这本复习手册汇总了 Eduqas GCSE 社会学考试必需的核心定量公式与关键理论“定理”。它涵盖出现在数据分析题中的研究方法计算，以及功能主义、马克思主义、女性主义、互动论和韦伯社会学的重要命题。把它当作考前速查工具，确保你既能驾驭数字，也能自信运用大思想。
1. Mean, Median, Mode and Range | 平均数、中位数、众数与极差
The mean is calculated by summing all values in a data set and dividing by the number of values. Sociologists use the mean to summarise average income, average household size or typical exam scores, but it is sensitive to extreme outliers, which can distort the picture.
平均数是将数据集中所有数值相加后除以数值个数。社会学家用平均数概括平均收入、家庭平均规模或典型考试成绩，但它对极端异常值敏感，可能扭曲真实情况。
Mean = (∑x) ÷ n
平均数 = (∑x) ÷ n
The median is the middle value when data are ordered from smallest to largest. If there are two middle values, take their mean. Median is preferred when a distribution is skewed, such as wealth data where a few billionaires inflate the mean.
中位数是将数据从小到大排序后位于中间的值。若有两个中间数，则取二者的平均数。当分布偏斜时更适合用中位数，比如财富数据中少数亿万富翁会拉高平均数。
The mode is the most frequently occurring value. It is useful for categorical data, for example the most common family type in a survey. Range equals the highest value minus the lowest value and gives a crude measure of spread.
众数是出现频率最高的值，适用于类别数据，比如问卷中最常见的家庭类型。极差等于最大值减去最小值，是衡量离散程度的粗略指标。
2. Percentage Change and Ratios | 百分比变化与比率
Percentage change shows how much a quantity has increased or decreased relative to its original size. It is frequently used to compare crime rates, educational attainment or social mobility trends across time.
百分比变化显示一个量相对于原始大小的增减幅度，常用于比较犯罪率、教育成就或社会流动性的跨时期趋势。
Percentage Change = [(New value − Old value) ÷ Old value] × 100
百分比变化 = [（新值 − 旧值）÷ 旧值] × 100
A ratio compares the magnitude of two quantities. In sociology, the gender pay gap is often expressed as a ratio of women's earnings to men's, and pupil-teacher ratios indicate resource levels in schools.
比率是比较两个数量的大小。在社会学中，性别薪酬差距常被表示为女性收入与男性收入的比值，而生师比则反映学校的资源水平。
Always check whether a percentage change is statistically meaningful or just a small fluctuation. Sociologists also distinguish between absolute and relative change: a 5% rise in educational achievement for disadvantaged pupils might still leave a wide relative gap.
必须判断百分比变化是否具有统计意义，抑或只是微小波动。社会学家还会区分绝对变化和相对变化：弱势学生教育成就上升 5%，但相对差距或许依然很大。
3. Sampling Methods and Representativeness | 抽样方法与代表性
A sample is a subset of the target population. Its representativeness determines whether findings can be generalised. Random sampling gives every member an equal chance of selection, reducing bias, while stratified sampling divides the population into known groups and samples proportionally.
样本是目标总体的子集。它的代表性决定了研究结果能否推广。随机抽样让每位成员有均等被选中的机会，减少偏差；分层抽样则先将总体划分为已知群体，再按比例抽取样本。
Quota sampling sets targets for certain characteristics but relies on researcher choice, which introduces selection bias. Snowball sampling uses initial contacts to recruit further participants, suitable for hidden populations but low in representativeness.
配额抽样为特定特征设定名额，但依赖研究者选择，会引入选择偏差。滚雪球抽样借助初始联系人招募更多参与者，适用于隐蔽群体但代表性低。
A theorem of social research: a larger, more representative sample increases the reliability and validity of data. However, practical constraints such as time and money often limit sample size.
社会研究定理：更大、更具代表性的样本能提升数据的可靠性与效度。但时间与金钱等实际条件常限制样本规模。
4. Functionalism: Social Order and Functions | 功能主义：社会秩序与功能
Functionalist Theorem 1: Society is a system of interconnected institutions – family, education, religion, economy – each performing functions that maintain social stability and value consensus.
功能主义定理1：社会是由家庭、教育、宗教、经济等互相联系的制度组成的系统，每一部分发挥功能以维持社会稳定和价值观共识。
Functionalist Theorem 2: Social facts, such as norms and values, exist outside the individual and exert constraint. Durkheim argued that even deeply personal acts like suicide are shaped by levels of social integration and moral regulation.
功能主义定理2：社会事实（如规范和价值观）存在于个体之外并施加约束。涂尔干认为，即便是自杀这样极其个人的行为，也受社会整合程度和道德规范的塑造。
Functionalist Theorem 3: Some phenomena that appear harmful may actually be functional. Merton distinguished between manifest functions (intended consequences) and latent functions (unintended, often hidden beneficial effects).
功能主义定理3：某些看似有害的现象可能实际上具有功能。默顿区分了显性功能（预期结果）和隐性功能（非预期的、往往隐藏的有益效果）。
Critics highlight that functionalism over-emphasises harmony, downplays power inequalities and struggles to explain rapid social change. Still, these theorems provide a lens for analysing how institutions fit together.
批评者指出，功能主义过度强调和谐，淡化权力不平等，且难以解释快速的社会变迁。然而，这些定理仍为分析制度间的配合提供了一个视角。
5. Marxism: Class Conflict and Capitalism | 马克思主义：阶级冲突与资本主义
Marxist Theorem 1: All history is the history of class struggle. In capitalist society, the bourgeoisie (owners of the means of production) exploit the proletariat (workers) by extracting surplus value.
马克思主义定理1：一切历史都是阶级斗争史。在资本主义社会，资产阶级（生产资料所有者）通过榨取剩余价值剥削无产阶级（工人）。
Marxist Theorem 2: The economic base (relations of production) shapes the superstructure – law, politics, education, media – which in turn legitimates the ruling-class ideology. This is often called the base-superstructure model.
马克思主义定理2：经济基础（生产关系）塑造上层建筑——法律、政治、教育、媒体——后者又使统治阶级意识形态合法化。这常被称为基础-上层建筑模型。
Marxist Theorem 3: Capitalist society inevitably contains contradictions, such as the drive for profit versus the immiseration of workers, leading to periodic crises and, in the long run, a revolutionary transformation to a classless society.
马克思主义定理3：资本主义社会必然包含矛盾，例如追逐利润与工人贫困化的对立，这导致周期性危机，长远来看将引发向无阶级社会的革命变革。
Modern Marxists, like Gramsci, introduced the concept of hegemony: ruling ideas become deeply embedded as 'common sense', making open coercion less necessary. These theorems remain powerful for analysing inequality today.
现代马克思主义者如葛兰西引入了霸权概念：统治阶级的思想深深内化为“常识”，使公开强迫变得不那么必要。这些定理至今仍是分析不平等的有力工具。
6. Feminism: Patriarchy and Gender Inequality | 女性主义：父权制与性别不平等
Feminist Theorem 1: Society is structured by patriarchy – a system of male domination operating in the family, workplace, media and politics. This patriarchy is not natural but socially constructed.
女性主义定理1：社会由父权制所建构——一种在家庭、职场、媒体和政治中运作的男性统治体系。这种父权制并非天然，而是社会建构的。
Feminist Theorem 2: Gender roles are learned through primary and secondary socialisation. Oakley argued that children are channelled into masculine and feminine behaviours through manipulation, canalisation and verbal appellations.
女性主义定理2：性别角色通过初级和次级社会化习得。奥克利指出，儿童通过操控、引导及言语称谓被导向男性化或女性化行为。
Feminist Theorem 3: The personal is political. Private sphere issues like housework, childcare and emotional labour are shaped by public power structures and therefore should be the subject of sociological analysis and political action.
女性主义定理3：个人的即政治的。家务、育儿和情感劳动等私人领域问题由公共权力结构所塑造，因此应成为社会学分析和政治行动的对象。
Liberal feminists seek legal and policy reforms, while radical feminists argue that patriarchy is the primary form of oppression, preceding class. Marxist feminists link women's subordination to capitalist exploitation. All share the theorem that gender inequality is structural, not individual.
自由派女性主义寻求法律和政策改革，激进女性主义主张父权制是最根本的压迫形式，先于阶级。马克思主义女性主义将女性从属地位与资本主义剥削联系起来。她们共享这样一条定理：性别不平等是结构性的，而非个人的。
7. Interactionism: Labelling and the Self | 互动论：标签与自我
Interactionist Theorem 1: Social reality is constructed through everyday interactions. People act toward things based on the meanings those things have for them, a core premise of Blumer's symbolic interactionism.
互动论定理1：社会现实通过日常互动建构。人们对事物采取行动是依据该事物对他们的意义，这是布鲁默符号互动论的核心前提。
Interactionist Theorem 2: The self is a social product. Cooley's looking-glass self states that we imagine how we appear to others, interpret their reactions and develop a self-concept. Mead emphasised the 'I' and the 'me' in role-taking.
互动论定理2：自我是社会产物。库利的镜中我指出，我们想象自己在他人眼中的形象，解读其反应，并形成自我概念。米德强调在角色扮演中“主我”与“客我”的作用。
Interactionist Theorem 3: Labelling can create a self-fulfilling prophecy. Becker argued that deviance is not a quality of the act but a label applied by powerful groups. Once labelled, individuals may internalise the label and act accordingly.
互动论定理3：标签可能导致自我实现预言。贝克尔认为，偏差并非行为本身的属性，而是强势群体贴上的标签。一旦被贴上标签，个体可能将其内化并据此行动。
Interactionism is criticised for downplaying structural factors like class and gender, but its theorems provide vital insight into identity, stigma and micro-level power in schools, families and criminal justice systems.
互动论被批评低估阶级、性别等结构性因素，但其定理为理解身份、污名以及学校、家庭和刑事司法系统中的微观权力提供了重要洞见。
8. Weber: Social Stratification and Power | 韦伯：社会分层与权力
Weberian Theorem 1: Stratification is multidimensional. Weber added status (social honour) and party (political power) to class (economic position). These three dimensions intersect but do not always align.
韦伯定理1：社会分层是多维度的。韦伯在阶级（经济地位）之外加入了地位（社会声望）和党派（政治权力）。这三个维度相互交叉，但并不总是一致。
Weberian Theorem 2: Class is a market situation: individuals with similar life chances in the labour and commodity markets share a class position. Unlike Marx, Weber did not see class as leading inevitably to collective action.
韦伯定理2：阶级是一种市场处境：在劳动市场与商品市场上拥有相似生活机会的个体处于同一阶级地位。与马克思不同，韦伯并不认为阶级必然导致集体行动。
Weberian Theorem 3: Authority is legitimate power. He distinguished traditional, charismatic and legal-rational authority. Bureaucracy, as the purest form of legal-rational authority, is efficient but creates an 'iron cage' of rules.
韦伯定理3：权威即合法化的权力。他区分了传统型、卡理斯玛型和法理型权威。官僚制作为最纯粹的法理型权威，虽高效却形成规则的“铁笼”。
These theorems remind you to consider not only income but also status groups (e.g. professions) and political influence when analysing inequality. The Eduqas exam often expects nuanced answers that go beyond a simple class model.
这些定理提醒你，分析不平等时不仅要考虑收入，还应关注地位群体（如专业人士）和政治影响力。Eduqas 考试常期待超越简单阶级模型的细致答案。
9. Social Mobility and Educational Achievement | 社会流动与教育成就
Social mobility refers to movement up or down the class structure. Intergenerational mobility compares parents' and children's social positions. Absolute mobility measures overall structural change, while relative mobility measures equality of opportunity.
社会流动指阶级结构中向上或向下的移动。代际流动比较父母与子女的社会地位。绝对流动衡量整体结构变化，相对流动则衡量机会平等程度。
Theorem: Education can facilitate social mobility, but Bourdieu's concept of cultural capital shows that middle-class families pass on advantages – language codes, attitudes, knowledge – that the education system rewards, reproducing inequality.
定理：教育可以促进社会流动，但布迪厄的文化资本概念表明，中产阶级家庭传递语言符码、态度、知识等优势，而教育体系奖励这些优势，从而再生产不平等。
Material deprivation (low income, poor housing) and cultural deprivation (lack of books, museum visits) both affect achievement. The pupil premium formula is a policy response: extra funding per disadvantaged pupil to narrow the attainment gap.
物质剥夺（低收入、住房差）和文化剥夺（缺少书籍、博物馆参观）都会影响成绩。学生津贴公式是一种政策回应：为每名弱势学生提供额外资金，以缩小成就差距。
Use the percentage change formula to analyse changes in free school meal (FSM) attainment gaps: calculate the gap in two different years, then express the change as a percentage. Always contextualise the numbers.
运用百分比变化公式分析免费校餐成绩差距的变化：计算两个不同年份的差距，再将变化表示为百分比。务必结合背景解读数字。
10. Crime Statistics and Dark Figure | 犯罪统计与暗数
lows comparison across areas and time periods, but it only reflects police-recorded crime.
每千人口犯罪率是一个标准度量：（记录在案的总犯罪数 ÷ 总人口）× 1,000。它便于跨地区、跨时期比较，但仅反映警方记录的犯罪。
Crime Rate per 1,000 = (Number of crimes ÷ Population) × 1,000
每千人口犯罪率 = （犯罪数量 ÷ 总人口）× 1,000
The dark figure of crime refers to offences that are not reported to or recorded by the police. Victim surveys like the Crime Survey for England and Wales reveal that recorded crime is only the tip of the iceberg.
犯罪暗数指未被报警或未被警方记录的犯罪行为。受害者调查如英格兰与威尔士犯罪调查显示，记录在案的犯罪仅是冰山一角。
Theorem: Official statistics are socially constructed. Interactionists argue that police decisions to stop, search and arrest are influenced by stereotypes, leading to systematic bias and over-representation of certain ethnic groups in crime figures.
定理：官方统计数据是社会建构的。互动论者指出，警察拦截、搜查和逮捕的决定受到刻板印象影响，导致系统性偏差，使某些族裔在犯罪数据中被过度代表。
Always interrogate the source of any statistic. Is it from police records, self-report studies or victim surveys? Each has different validity issues, and a skilled sociological analysis weighs them all.
必须审视任何统计数据的来源。它是来自警方记录、自陈报告还是受害者调查？各有效度问题，精湛的社会学分析会予以综合权衡。
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