📚 SQA Year 12 Sociology: Formula & Theorem Quick Reference Handbook | SQA 高年级 12 社会学：公式定理速查手册
Sociology is often perceived as a qualitative discipline, yet at Year 12 level, SQA candidates are expected to handle quantitative evidence with precision. Rates, indices, and statistical relationships are the ‘formulae’ of social analysis, enabling you to measure inequality, track social change, and evaluate theoretical claims. This handbook compiles the essential numerical and conceptual tools you will encounter across topics such as social stratification, crime, education, and the family. Each entry presents a clear expression, followed by its sociological meaning and a worked example where applicable. Use these as revision anchors and as a bridge between raw data and critical argument.
社会学常被视为定性学科，但在 12 年级 SQA 课程中，考生需要精确处理量化证据。比率、指数和统计关系就是社会分析的“公式”，它们帮助你衡量不平等、追踪社会变迁并评价理论主张。本手册汇集了你在社会分层、犯罪、教育和家庭等主题中会遇到的关键数字与概念工具。每个条目先给出清晰表达式，再解释其社会学意义，并附有实例。可将这些内容作为复习的锚点，以及连接原始数据与批判性论证的桥梁。
1. Social Mobility Rate | 社会流动率
The social mobility rate measures the proportion of individuals who move from one social class to another compared to their parents’ class position. The basic formula is: Mobility Rate = (Number of individuals in a different class from parents ÷ Total sample) × 100. Absolute mobility simply counts all moves, while relative mobility compares the chances of moving up or down for different class origins. Sociologists use this to test the ‘openness’ of society. A high rate suggests a meritocratic system; a low rate points to class reproduction.
社会流动率衡量个体与其父母所处社会阶级不同的比例。基本公式为：流动率 =（与父母阶级不同的个体数 ÷ 样本总数）× 100。绝对流动只计算所有移动，而相对流动比较不同阶级出身者上升或下降的机会。社会学家用它检验社会的“开放性”。高流动率暗示精英统治体系；低流动率则指向阶级再生产。
2. Divorce Rate | 离婚率
The crude divorce rate is expressed as the number of divorces per 1,000 people in the population per year: Crude Divorce Rate = (Total divorces in a year ÷ Mid-year population) × 1,000. A more refined measure is the divorce rate per 1,000 married people. However, sociologists also construct cohort-specific rates, such as the percentage of marriages ending in divorce after 15 years. These rates are fundamental to evaluating the ‘crisis of the family’ thesis and the impact of legal changes like the Divorce Reform Act.
粗离婚率指每年每 1,000 人口中的离婚对数：粗离婚率 =（全年离婚总数 ÷ 年中总人口）× 1,000。更精细的指标是每 1,000 已婚者的离婚率。不过，社会学家还会构建特定同期群比率，比如结婚 15 年后以离婚告终的婚姻百分比。这些比率是评价“家庭危机”论以及《离婚改革法》等法律变化影响的基础。
3. Poverty Rate (Absolute & Relative) | 贫困率（绝对与相对）
The absolute poverty line is based on the minimum income needed for subsistence; those below it are counted as poor. Relative poverty is set at 60% of median household income. The formula for the relative poverty rate is: Poverty Rate = (Number of households with income below 60% of median ÷ Total households) × 100. After housing costs, the equation adjusts income accordingly. The indicator underpins debates on the welfare state: if the rate rises, it may signal increasing inequality or inadequate social safety nets.
绝对贫困线基于维持生存所需的最低收入；收入低于该线者视为贫困。相对贫困则设定为家庭收入中位数的 60%。相对贫困率公式为：贫困率 =（收入低于中位数 60% 的家庭数 ÷ 家庭总数）× 100。若考虑住房成本，则需相应调整收入。该指标支撑着福利国家争论：若比率上升，可能意味着不平等加剧或社会安全网不足。
4. Unemployment Rate (ILO Definition) | 失业率（国际劳工组织定义）
The internationally standardised unemployment rate is: Unemployment Rate = (Number of people actively seeking work and available to start ÷ Labour force) × 100. The labour force includes both employed and unemployed. Sociologists distinguish this from the claimant count, which only includes those receiving benefits. The unemployment rate is crucial for examining the lived experience of the underclass, anomie, and strain theory. Long-term unemployment rate focuses on those out of work for over a year.
国际标准化的失业率为：失业率 =（积极求职且可立即上岗者人数 ÷ 劳动力人口）× 100。劳动力人口包括就业和失业者。社会学家将其与只涵盖领取救济金者的申领人数区别开来。失业率对审视底层阶级的生活体验、失范和紧张理论至关重要。长期失业率则聚焦失业超过一年的人群。
5. Crime Rate | 犯罪率
The official crime rate per 1,000 population is: Crime Rate = (Number of recorded crimes ÷ Population) × 1,000. Sociologists recognise the dark figure of crime — offences not reported or recorded. The British Crime Survey (now CSEW) provides an alternative victimisation rate: Victimisation Rate = (Number of people reporting a crime in survey ÷ Survey respondents) × 100. Comparing these rates reveals the gap between police statistics and lived reality, a cornerstone of labelling theory and institutional deviance studies.
官方犯罪率（每千人）公式为：犯罪率 =（记录在案的案件数 ÷ 人口数）× 1,000。社会学家认识到犯罪黑数——即未被报告或记录的案件。英国犯罪调查（现为 CSEW）提供了替代的受害率：受害率 =（调查中报告犯罪的人数 ÷ 受访者总数）× 100。比较二者可以揭示警方统计与现实生活之间的差距，这是标签理论和制度越轨研究的基石。
6. Gini Coefficient | 基尼系数
The Gini coefficient condenses the income distribution of a population into a single number between 0 and 1 (or 0 and 100). A value of 0 signifies perfect equality; 1 indicates perfect inequality. While the formula involves the Lorenz curve area calculation, for the exam you only need to interpret it: Gini = A / (A + B), where A is the area between the line of equality and the Lorenz curve, and B is the area under the Lorenz curve. Longitudinal Gini trends test the ‘trickle-down’ effect and the impact of austerity.
基尼系数将人口收入分布浓缩为一个 0 到 1（或 0 到 100）之间的数字。0 表示完全平等，1 表示完全不平等。虽然公式涉及洛伦兹曲线面积计算，但考试中只需解释：基尼系数 = A / (A + B)，其中 A 是均等线与洛伦兹曲线间的面积，B 是洛伦兹曲线下的面积。追踪基尼系数变化可以检验“涓滴效应”和紧缩政策的影响。
7. Relative Deprivation Index | 相对剥夺感指数
Relative deprivation is measured through multi-item scales. A simple form is the deprivation score: Deprivation Score = Number of enforced lacks (e.g., unable to afford heating, one week’s holiday, etc.) ÷ Total number of items considered necessities. Townsend’s index pioneered this approach. The score quantifies the gap between what is socially accepted and what individuals can achieve. It is used in poverty studies to show that poverty is not just about income but about inability to participate in community life.
相对剥夺感通过多项目量表测量。简单形式为剥夺分数：剥夺分数 = 被迫缺乏的项目数（如无力支付取暖费、一周假期等）÷ 被视为必需品的项目总数。Townsend 指数率先采用此法。该分数量化了社会认可标准与个体实况之间的差距。在贫困研究中用于说明贫困不仅是收入问题，更是无力参与社区生活的问题。
8. Social Network Density | 社会网络密度
In interactional sociology, network density measures the cohesion of a group: Density = (Number of actual ties ÷ Number of possible ties). In an undirected network of n individuals, possible ties = n(n − 1) ÷ 2. For example, a study of elite networks might reveal high density among public school alumni, supporting the ‘old boys’ network’ thesis. Density can explain collective action, social capital, and the diffusion of norms.
在互动社会学中，网络密度衡量群体的凝聚力：密度 =（实际联系数 ÷ 可能联系数）。在 n 名个体构成的无向网络中，可能联系数为 n(n − 1) ÷ 2。例如，对精英网络的研究可能揭示公学校友之间的联系密度很高，从而支持“老男孩网络”论。密度有助于解释集体行动、社会资本和规范扩散。
9. Cultural Capital Metric | 文化资本度量
Bourdieu’s cultural capital is operationalised through participation in highbrow activities. A typical metric is the Cultural Capital Index: CCI = (Sum of cultural activities engaged in ÷ Total list of activities) × 100. Activities might include theatre attendance, classical music listening, and museum visits. This index correlates with educational achievement and social class, revealing how cultural resources are converted into advantage. Changes in the index over time help assess whether cultural boundaries are blurring.
布迪厄的文化资本通过高雅活动参与度进行操作性定义。典型指标为文化资本指数：CCI =（参与的文化活动总和 ÷ 活动列表总数）× 100。活动可包括去剧院、听古典音乐和参观博物馆。该指数与教育成就和社会阶级相关，揭示文化资源如何转化为优势。指数随时间的变化有助于评估文化边界是否在模糊。
10. Educational Achievement Gap | 教育成就差距
The achievement gap is calculated as the percentage point difference in attainment between two groups. For instance, the FSM gap: FSM Gap = (% of non-Free School Meals pupils achieving 5 A*-C grades) − (% of FSM pupils achieving the same). A similar formula applies to gender, ethnicity, or class. This gap is central to social policy; the Pupil Premium was designed to close it. Tracking the gap over Key Stages provides evidence on the processes of labelling, streaming, and self-fulfilling prophecy.
成就差距计算为两组之间达标百分点的差值。例如，免费校餐（FSM）差距：FSM 差距 =（未享受免费校餐学生达到 5 门 A*-C 等级的比例）−（享受 FSM 学生达到同等水平的比例）。类似公式适用于性别、族群或阶级。这一差距是社会政策的核心；“学生津贴”政策旨在缩小差距。追踪关键学段的差距变化，可为标签、分轨与自证预言等过程提供证据。
11. Gender Pay Gap | 性别薪酬差距
The gender pay gap is the difference in average hourly earnings between men and women, expressed as a percentage of men’s earnings: GPG = [(Mean hourly earnings of men − Mean hourly earnings of women) ÷ Mean hourly earnings of men] × 100. The median is often preferred to reduce distortion by very high earners. The UK also reports bonus gaps. The GPG is a direct measure of workplace inequality and fuels feminist analyses of the devaluation of ‘women’s work’ and horizontal/vertical segregation.
性别薪酬差距指男女平均时薪的差异，表达为男性收入的一个百分比：GPG = [（男性平均时薪 − 女性平均时薪）÷ 男性平均时薪] × 100。通常偏好中位数以减少极高收入者的扭曲。英国还报告奖金差距。GPG 是工作场所不平等的直接量度，支撑着女性主义对“女性工作”贬值以及水平/垂直隔离的分析。
12. Class Reproduction and the Odds Ratio | 阶级再生产与优比比率
Sociologists use odds ratios to show the relative chances of a class outcome. For example, comparing the odds of a service-class child entering university versus a working-class child: Odds Ratio = (A/C) ÷ (B/D), where A = service-class entrants, B = working-class entrants, C = service-class non‑entrants, D = working-class non‑entrants. An odds ratio of 1 means no difference; above 1 indicates higher odds for the service class. This precise measure is vital for evaluating cultural and economic capital theories against meritocracy.
社会学家运用优比比率展示阶级结果的相对机会。例如，比较高服务阶级子女与工人阶级子女进入大学的机会：优比比率 = (A/C) ÷ (B/D)，其中 A = 服务阶级进入者，B = 工人阶级进入者，C = 服务阶级未进入者，D = 工人阶级未进入者。优比比率为 1 表示无差异；大于 1 表明服务阶级有更高机会。这一精确指标对评价文化经济资本理论与精英统治论至关重要。
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