📚 IGCSE CAIE Sociology: Formula and Theorem Quick Revision Handbook | IGCSE CAIE 社会学：公式定理速查手册
This revision handbook does not treat sociology as a subject of physics-style equations, but it does contain repeatable formulas, ratios and theoretical “theorems” that CAIE expects you to apply in data-response and essay questions. The formulas below are simplified for IGCSE use and should be quoted with units where relevant.
本速查手册并不把社会学当作物理式公式学科，但它确实包含 CAIE 希望你在数据分析题和论述题中应用的可重复公式、比率与理论 “定理”。以下公式已按 IGCSE 要求简化，引用时应注明单位。
1. Core Quantitative Formulas in Sociological Research | 社会学研究中的核心量化公式
The birth rate measures the number of live births per 1,000 people in a year. It is a standard demographic indicator, often used to compare industrialised and developing societies.
出生率衡量一年中每 1,000 人中的活产婴儿数。它是标准的人口指标，常用于比较工业化社会与发展中社会。
Birth rate = (Live births ÷ Mid-year population) × 1,000
The death rate is calculated in the same way, using the number of deaths. The natural increase of a population can be found by subtracting the death rate from the birth rate.
死亡率以同样方式计算，但使用死亡人数。人口自然增长率可用出生率减去死亡率得到。
Death rate = (Deaths ÷ Mid-year population) × 1,000
Natural increase = Birth rate − Death rate
2. Demographic Rates and Ratios | 人口统计比率与比例
The total fertility rate (TFR) is the average number of children a woman would have during her reproductive years. It is not a simple count of births in one year, but it is often converted into a formula for comparison.
总和生育率（TFR）是一名妇女在育龄期内平均预期生育的子女数。它不是某一年出生数的简单计数，但常被转化为可比较的公式。
TFR = Σ (Age-specific fertility rates)
The dependency ratio compares the economically dependent population (under 15 and over 64) with the working-age population (15–64). A high ratio suggests greater pressure on welfare, pensions and healthcare.
抚养比将经济上依赖的人口（15 岁以下和 64 岁以上）与劳动年龄人口（15–64 岁）进行比较。比率高说明福利、养老金和医疗压力更大。
Dependency ratio = [(Population aged 0–14 + Population aged 65+) ÷ Population aged 15–64] × 100
3. Sampling and Representativeness | 抽样与代表性
A sampling fraction tells you what proportion of the target population is included in the sample. Sociologists must choose a sampling method that maximises representativeness while staying practical.
抽样比告诉你目标总体中有多大比例被纳入样本。社会学家必须选择一种在保持可行性的同时最大化代表性的抽样方法。
Sampling fraction = Sample size ÷ Target population size
Sample proportion (%) = (Number in sample with characteristic ÷ Total sample size) × 100
Random sampling gives every member of the sampling frame an equal chance of selection. Stratified random sampling divides the population into known groups, then samples randomly within each group.
随机抽样使抽样框中的每个成员都有相等的机会被选中。分层随机抽样先将总体划分为已知群体，然后在各群体内随机抽样。
4. Measures of Central Tendency | 集中趋势量数
The mean is the arithmetic average and is sensitive to extreme values. The median is the middle value in an ordered list and is less affected by outliers. The mode is the most frequent value.
均数是算术平均数，对极端值敏感。中位数是排序后位于中间的数值，受异常值影响较小。众数是出现频率最高的数值。
Mean = Σx ÷ n
The range is the simplest measure of dispersion: it subtracts the smallest value from the largest value. It can hide the distribution of values in between.
全距是最简单的离散程度量数：用最大值减去最小值。它可能掩盖中间数值的分布情况。
Range = Highest value − Lowest value
5. Key Theoretical “Theorems”: Functionalism | 关键理论 “定理”：功能主义
Functionalism works like a theorem of social order: if institutions such as the family, education and religion perform their functions, then society remains stable. Social change is usually slow and evolutionary.
功能主义如同一个社会秩序 “定理”：如果家庭、教育和宗教等制度发挥其功能，那么社会就保持稳定。社会变迁通常是缓慢且渐进的。
A key formula-like idea is: Social stability = Shared norms + Effective socialisation + Institutional integration. Durkheim used organic solidarity to explain how specialised roles bind people together.
一个类似公式的核心观点是：社会稳定 = 共同规范 + 有效社会化 + 制度整合。涂尔干用有机团结解释专门化角色如何将人们联系在一起。
Social stability = Shared norms + Effective socialisation + Institutional integration
6. Marxist and Weberian Frameworks | 马克思主义与韦伯主义框架
Marxism offers a conflict “theorem”: class inequality is generated by the ownership and non-ownership of the means of production. The bourgeoisie exploits the proletariat by extracting surplus value.
马克思主义提供了一种冲突 “定理”：阶级不平等由生产资料的所有权与无所有权所产生。资产阶级通过榨取剩余价值来剥削无产阶级。
Class position ≈ Relationship to the means of production
Max Weber added two extra dimensions to social stratification: status (social honour) and party (power). So class alone cannot explain all inequality.
韦伯为社会分层增加了两个维度：地位（社会声望）和政党（权力）。因此单靠阶级无法解释所有不平等。
Life chances = Class + Status + Party
7. Feminist and Interactionist Perspectives | 女性主义与互动论视角
Feminist theory treats patriarchy as a structural cause of gender inequality. It can be expressed as a principle: gender inequality is reproduced when power, resources and expectations are organised in favour of men.
女性主义理论将父权制视为性别不平等的结构性原因。它可以表述为一个原则：当权力、资源和期望以有利于男性的方式组织时，性别不平等就被再生产。
Gender inequality ≈ Patriarchal structure + Gendered socialisation
Interactionism focuses on small-scale meanings and labels. The labelling theorem says: if a powerful group labels an act as deviant, then the individual may adopt that label and repeat the behaviour.
互动论关注小规模的意义与标签。标签定理指出：如果强势群体将某种行为贴上偏差标签，那么个体可能接受该标签并重复该行为。
Deviant career = Label + Internalisation + Amplification
8. Social Stratification Measures | 社会分层测量
Social class can be measured by occupation, income, wealth and lifestyle. The Registrar General’s scale and the NS-SEC are used in the UK to classify occupations. In IGCSE answers, you can use a simple formula linking class to occupation and market position.
社会阶级可以通过职业、收入、财富和生活方式来测量。英国使用注册总署量表与 NS-SEC 对职业进行分类。在 IGCSE 答案中，你可以用一个简单公式把阶级与职业和市场地位联系起来。
Social class ≈ Occupation + Income + Wealth + Status
Absolute poverty means lacking the minimum resources for survival. Relative poverty means being poor compared with the average standard of living in a society.
绝对贫困指缺乏维持生存的最低资源。相对贫困指与社会平均生活水平相比处于贫困状态。
Poverty line = Minimum income required for basic needs
9. Crime and Deviance Statistics | 犯罪与偏差统计
The official crime rate is usually expressed as recorded offences per 1,000 people. It is an imperfect measure because many crimes are not reported or recorded; this is called the dark figure of crime.
官方犯罪率通常以每 1,000 人中的记录犯罪数来表示。它是不完善的测量，因为许多犯罪未被报案或记录；这被称为犯罪黑数。
Crime rate = (Recorded offences ÷ Total population) × 1,000
Victim surveys and self-report studies can uncover hidden crime. The formula for a self-report rate is the number of admitted offences divided by the number of respondents, often multiplied by 100.
受害者调查和自我报告研究可以揭示隐性犯罪。自我报告率的公式是承认的犯罪数除以受访人数，通常乘以 100。
Self-report rate = (Admitted offences ÷ Number of respondents) × 100
10. Research Ethics and Validity Principles | 研究伦理与效度原则
Validity means the research measures what it claims to measure; reliability means the research can be repeated and produce consistent results. There is often a trade-off between validity and reliability in sociological methods.
效度指研究确实测量了它声称要测量的东西；信度指研究可以重复并产生一致结果。社会学方法中，效度与信度之间常常存在权衡。
Ethical principles can be remembered with the “PID” rule: Privacy, Informed consent, and Do no harm. These principles apply to questionnaires, interviews, observations and experiments.
伦理原则可用 “PID” 规则记忆：隐私（Privacy）、知情同意（Informed consent）和不伤害（Do no harm）。这些原则适用于问卷、访谈、观察和实验。
Research quality = Validity + Reliability + Ethics
11. Education and Family Indicators | 教育与家庭指标
Educational attainment can be compared using the percentage achieving five or more GCSEs at grade 4/C or above. The formula is simply the number of students reaching the benchmark divided by the total number of students, multiplied by 100.
教育成就可以用达到五门及以上 GCSE 4/C 或以上等级的学生百分比来比较。公式为达到基准的学生人数除以学生总数，再乘以 100。
Attainment rate = (Students reaching benchmark ÷ Total students) × 100
In family sociology, the divorce rate is a common indicator. It is usually expressed as the number of divorces per 1,000 married people or per 1,000 population, depending on the source.
在家庭社会学中，离婚率是常用指标。通常表示为每 1,000 名已婚者或每 1,000 人中的离婚数，取决于资料来源。
Divorce rate = (Divorces ÷ Married population) × 1,000
12. Checklist for Exam Application | 考试应用速查清单
Before applying any formula, check whether the question asks for a rate, a percentage, a measure of central tendency or a theoretical explanation. Many CAIE marks are awarded for interpretation, not just calculation.
在应用任何公式之前，检查题目要求的是比率、百分比、集中趋势量数还是理论解释。CAIE 的许多分值颁发给解释，而不仅仅是计算。
- Identify the correct formula and write it out.
识别正确的公式并写出。 - Substitute the data carefully, keeping the same units.
仔细代入数据，保持单位一致。 - Interpret the result: say what it means for the sociological question.
解释结果：说明它对社会学问题的意义。 - Evaluate: mention validity, reliability and representativeness limits.
评估：提及效度、信度和代表性的局限。
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