📚 Year 11 CCEA Sociology: Formula & Theorem Quick Reference Handbook | CCEA 11 年级社会学：公式定理速查手册
This quick reference guide brings together the essential statistical formulas, key theoretical ‘theorems’ and methodological principles that every Year 11 CCEA Sociology student needs to master. Designed as a handy revision tool, it bridges the gap between quantitative research methods and the core theoretical frameworks you encounter in papers on socialisation, inequality and social structures.
本速查手册汇集了每一位 CCEA 11 年级社会学学生必须掌握的核心统计公式、重要理论’定理’以及方法论原则。它作为便捷的复习工具，在定量研究方法与社会化、不平等、社会结构等试卷中的核心理论框架之间架起了桥梁。
1. Statistical Formulas in Sociological Research | 社会学研究中的统计公式
Sociologists use mathematical tools to transform raw data into meaningful findings. The formulas below are not abstract maths; they are the lens through which we identify patterns of inequality, trends in social mobility and the reliability of our measurements. Mastering them helps you interpret graphs, tables and questionnaire results accurately.
社会学家运用数学工具将原始数据转化为有意义的发现。以下公式并非抽象的数学运算，而是我们识别不平等模式、社会流动趋势和测量信度的透镜。掌握它们能帮助你准确解读图表、表格和问卷结果。
2. Measures of Central Tendency: Mean, Median and Mode | 集中趋势测量：平均值、中位数和众数
The mean is calculated by adding all values together and dividing by the total number of cases. It is sensitive to extreme scores and works best with continuous data such as income or exam marks.
平均值通过将所有数值相加再除以个案总数得出。它对极端值敏感，最适合用于收入或考试成绩等连续型数据。
Mean (x̄) = (Σx) ÷ n
The median is the middle value when all scores are arranged in order; it is resistant to outliers and is often preferred for distributions such as household wealth.
中位数是将所有分数排序后位于中间的值；它不受极端值影响，常用于家庭财富等分布。
The mode is the most frequently occurring value. It is the only measure usable with nominal data, such as ‘type of family structure’.
众数是出现频率最高的值。它是唯一可用于定类数据（如’家庭结构类型’）的集中趋势测量。
3. Measure of Dispersion: Range | 离散度测量：极差
Range tells us the spread of data by subtracting the lowest value from the highest. A large range signals high inequality or variation within a sample, while a small range suggests homogeneity.
极差通过用最大值减去最小值显示数据的离散程度。极差大表示样本内部不平等或变异较大，极差小则表示同质性高。
Range = Highest Value − Lowest Value
For example, if weekly pocket money among Year 11 pupils ranges from £2 to £40, the range of £38 reveals stark differences in family resources.
例如，如果11年级学生的每周零花钱从2英镑到40英镑不等，那么38英镑的极差揭示了家庭资源方面的显著差异。
4. Percentages and Percentage Change | 百分比与百分比变化
Percentages standardise comparisons by expressing a part out of 100. This is vital when comparing groups of different sizes, such as the proportion of girls and boys achieving Grade 5+ in Maths across two schools.
百分比以占100的比例实现标准化对比。这在比较不同规模群体时至关重要，比如跨校比较获得数学5级及以上成绩的男女生比例。
Percentage = (Part ÷ Whole) × 100
Percentage change measures growth or decline over time, which is crucial for examining trends in crime rates, divorce statistics or educational attainment.
百分比变化衡量随时间推移的增长或下降，这对于研究犯罪率、离婚统计或教育成就的趋势至关重要。
Percentage Change = ((New Value − Old Value) ÷ |Old Value|) × 100
5. Ratios and Rates per 1,000 | 比率与每千人率
Ratios express the relationship between two quantities, such as the dependency ratio (number of dependents per 100 working-age people). Rates per 1,000 allow sociologists to compare how common an event is across populations of different sizes.
比率表示两个数量之间的关系，例如抚养比（每100名劳动适龄人口对应的受抚养人数）。每千人率使社会学家能够比较不同规模人口中某一事件的普遍程度。
Rate per 1,000 = (Number of Events ÷ Total Population) × 1,000
The birth rate, crime rate and divorce rate are all expressed per 1,000 people to make cross-national or historical comparison meaningful.
出生率、犯罪率和离婚率均以每千人表示，以便进行有意义的跨国或历史比较。
6. Reliability and Validity as Methodological Theorems | 作为方法论定理的信度与效度
Reliability is the ‘theorem’ that a method yields consistent results on repeated trials. If a questionnaire produces the same answers from similar respondents under identical conditions, it is said to be reliable. Unreliable data, like a poorly designed self-completion survey with ambiguous questions, undermines sociological conclusions.
信度是一条’定理’，即一种方法在重复测试中能够得出一致结果。如果一份问卷在相同条件下对相似受访者施测得到相同答案，则可称为具有信度。不可靠的数据，例如一份设计拙劣、问题模糊的自填式问卷，会削弱社会学结论。
Validity is the theorem that a tool measures what it claims to measure. An in-depth interview might yield high validity because it captures participants’ true meanings, whereas a closed question may lack validity if it forces oversimplified answers.
效度是一条’定理’，即工具能够测量其声称要测量的内容。深度访谈可能具有高效度，因为它捕捉了参与者的真实含义，而封闭式问题如果迫使答案过于简化，则可能缺乏效度。
7. Key Theorems of Functionalism | 功能主义关键定理
Functionalism views society as a system of interdependent parts. One core theorem is that every social institution – family, education, religion – performs functions that maintain social stability and value consensus.
功能主义将社会视为一个相互依存部分的系统。其核心定理之一是每个社会制度——家庭、教育、宗教——都履行着维持社会稳定和价值共识的功能。
Durkheim’s theorem of anomie states that rapid social change weakens norms, leading to a breakdown of social regulation and a rise in deviance. Parsons’ functional prerequisites theorem identifies adaptation, goal attainment, integration and latency (AGIL) as essential for any society’s survival.
涂尔干的失范定理指出，急剧的社会变迁会弱化规范，导致社会调控崩溃和越轨行为上升。帕森斯的功能先决条件定理提出，适应、目标达成、整合和模式维持（AGIL）是任何社会存续的必要条件。
8. Key Theorems of Marxism | 马克思主义关键定理
The base-superstructure theorem asserts that the economic base (relations of production) shapes the superstructure – family, law, media, religion – which in turn legitimises class inequality.
经济基础-上层建筑定理主张，经济基础（生产关系）塑造了上层建筑——家庭、法律、媒体、宗教——而上层建筑反过来使阶级不平等合法化。
Marx’s theorem of class polarisation predicts that capitalism concentrates wealth in a shrinking bourgeoisie while expanding a pauperised proletariat, eventually leading to revolutionary class consciousness.
马克思的阶级两极分化定理预言，资本主义会将财富集中到不断缩小的资产阶级手中，同时扩大贫困化的无产阶级，最终导致革命的阶级意识。
The theorem of alienation describes how workers lose control over the product, process, fellow workers and their own creative potential in capitalist production.
异化定理描述了工人在资本主义生产中如何丧失对产品、生产过程、同伴以及自身创造潜能的控制。
9. Key Theorems of Feminism | 女权主义关键定理
The core theorem of radical feminism states that patriarchy – a system of male domination – is the primary structure shaping gender inequality across all institutions, from the household to the state.
激进女权主义的核心定理指出，父权制——一种男性统治体系——是塑造从家庭到国家所有制度中性别不平等的主要结构。
Liberal feminists propose that sex-role socialisation and discriminatory laws create inequality, and that legal reform and equal opportunity policies can dismantle these barriers. Intersectional feminism adds the theorem that gender, class and race are interlocking systems of oppression that cannot be examined in isolation.
自由女权主义者提出，性别角色社会化和歧视性法律制造了不平等，而法律改革和机会平等政策可以消除这些障碍。交织性女权主义补充了一条定理：性别、阶级和种族是相互锁定的压迫体系，不能孤立地进行审视。
10. Theorems of Symbolic Interactionism | 符号互动论定理
The looking-glass self theorem (Cooley) claims our self-concept arises from how we imagine others perceive us. Labelling theory is the theorem that a deviant label, once successfully applied, becomes a master status that shapes identity and future behaviour (Becker).
镜中我定理（库利）认为，我们的自我概念源于我们想象他人如何看待我们。标签理论是一条定理：越轨标签一旦被成功贴上，就会成为主导地位，塑造身份认同和未来行为（贝克尔）。
Goffman’s dramaturgical theorem suggests social life is a performance, with actors managing impressions on a front stage while revealing a more authentic self backstage.
戈夫曼的拟剧定理指出，社会生活是一场表演，行动者在’前台’进行印象管理，而在’后台’展现更真实的自我。
11. Theorems of the Socialisation Process | 社会化过程定理
Primary socialisation theorem: the family is the crucial first agent transmitting basic norms, language and cultural values. Secondary socialisation theorem: institutions like schools, peer groups and mass media build on this foundation, teaching universalistic standards and role expectations.
初级社会化定理：家庭是传递基本规范、语言和文化价值观的关键首要媒介。次级社会化定理：学校、同辈群体和大众媒体等制度在此基础上延伸，教授普遍性标准和角色期待。
Hidden curriculum theorem (Bowles & Gintis) holds that schooling subtly instils acceptance of hierarchy, punctuality and obedience, mirroring workplace relations under capitalism.
隐性课程定理（鲍尔斯与金蒂斯）认为，学校教育潜移默化地灌输对等级制、守时和服从的接受，这反映了资本主义下的工作关系。
12. Measuring Social Stratification and Inequality Indices | 社会分层测量与不平等指数
The absolute poverty line formula is a cut-off set at a minimum income required to meet basic needs. Relative poverty is defined as living below 60% of the median household income, a widely used inequality index.
绝对贫困线公式是满足基本需求所需的最低收入门槛。相对贫困被定义为收入低于家庭收入中位数的60%，这是一个广泛使用的不平等指数。
Relative Poverty Threshold = 0.6 × Median Equivalised Household Income
The intergenerational mobility index reflects the ‘theorem’ that class origins still powerfully predict educational outcomes and occupational destinations. Using such indices, sociologists test claims of meritocracy and uncover the persistence of life-chance gaps.
代际流动性指数反映了一条’定理’：阶级出身仍然强有力地预测教育成就和职业归宿。社会学家利用这些指数检验贤能主义的宣称，并揭示生活机会差距的持续存在。
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