AQA GCSE Sociology Formula & Theorem Quick Reference | AQA GCSE 社会学公式定理速查手册

📚 AQA GCSE Sociology Formula & Theorem Quick Reference | AQA GCSE 社会学公式定理速查手册

This quick-reference handbook brings together the most important formulas and theoretical ‘theorems’ you will encounter in Year 10 AQA Sociology. From demographic rates to the central arguments of key thinkers, every entry is presented in a bilingual, mirrored format so you can revise both content and terminology simultaneously. Use it to strengthen your AO1 knowledge and to decode exam questions that require calculation or application of sociological ideas.

这本速查手册汇集了 Year 10 AQA 社会学中最关键的公式和理论‘定理’。从人口统计率到核心思想家的中心论述，每一条目都以双语对照的形式呈现，让你可以同时复习内容和术语。用它来巩固 AO1 知识，并解读需要计算或运用社会学观点的考题。

1. Demographic Formulas | 人口学公式

Demographic measures quantify population change and are essential for analysing family size, migration patterns and the consequences of policy. Always check whether the denominator refers to total population, women of childbearing age or a specific subgroup.

人口学指标量化人口变化，是分析家庭规模、迁移模式以及政策后果的基础。务必确认分母是指总人口、育龄女性还是特定子群体。

Crude Birth Rate (CBR) = (Number of live births / Total mid‑year population) × 1000

粗出生率 (CBR) = (活产婴儿数 / 年中总人口) × 1000——反映每千人中出生人数，是判断人口更替水平的基础。

Crude Death Rate (CDR) = (Number of deaths / Total mid‑year population) × 1000

粗死亡率 (CDR) = (死亡人数 / 年中总人口) × 1000——显示每千人死亡水平，受年龄结构影响较大。

General Fertility Rate (GFR) = (Number of live births / Number of women aged 15–44) × 1000

一般生育率 (GFR) = (活产婴儿数 / 15–44 岁女性人数) × 1000——比粗出生率更精确，因为它只聚焦可能生育的群体。

Infant Mortality Rate (IMR) = (Deaths of infants under 1 year / Total live births) × 1000

婴儿死亡率 (IMR) = (1 岁以下婴儿死亡数 / 活产婴儿总数) × 1000——被视为衡量社会整体健康水平的关键指标。

Rate of Natural Increase (RNI) = (CBR – CDR) or expressed per 1000 population

自然增长率 (RNI) = (粗出生率 – 粗死亡率) 或表示为每千人中——用于判断人口在无迁移情况下的增减趋势。

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2. Family Change Indicators | 家庭变迁指标

Formulas for marriage, divorce and cohabitation allow sociologists to measure the changing shape of family life. They often reveal long‑term trends such as secularisation and the rise of individual choice.

婚姻、离婚与同居的相关公式使社会学家得以测量家庭生活的变化形态。它们常揭示世俗化与个人选择兴起等长期趋势。

Marriage Rate = (Number of marriages / Total population) × 1000

结婚率 = (结婚数量 / 总人口) × 1000——在 AQA 考题中常用来讨论婚姻制度的衰微。

Divorce Rate = (Number of divorces / Number of married couples) × 1000

离婚率 = (离婚对数 / 已婚夫妇对数) × 1000——注意分母是已婚夫妇而非全体人口，这点易错。

Percentage of lone‑parent families = (Number of lone‑parent households / Total households with children) × 100

单亲家庭百分比 = (单亲家庭户数 / 有孩子的家庭总户数) × 100——可用于评价 New Right 人士对福利依赖的忧虑。

Remarriage Rate = (Number of remarriages / Divorced and widowed population) × 1000

再婚率 = (再婚人数 / 离婚和丧偶人口) × 1000——体现社会对重组家庭的接纳程度。

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3. Crime Statistics Formulas | 犯罪统计公式

Official crime data need to be interpreted with care, as they depend on recording practices and public reporting. These formulas convert raw numbers into meaningful rates that can be compared across time and place.

官方犯罪数据需谨慎解读，因为它们依赖于记录实践和公众报案。以下公式把原始数字转换成可跨时空比较的有意义比率。

Crime Rate = (Number of recorded crimes / Total population) × 100 000

犯罪率 = (记录在案的犯罪数 / 总人口) × 100 000——使用每十万人口可使地区间比较更直观。

Clear‑up Rate = (Number of crimes solved / Number of recorded crimes) × 100%

破案率 = (已破案件数 / 记录在案的犯罪数) × 100%——高破案率不一定代表低犯罪率，而是警方效能的一个侧面。

Victimisation Rate = (Number of victims / Total population) × 1000

受害率 = (受害者人数 / 总人口) × 1000——常取自 British Crime Survey (CSEW)，弥补警方记录的暗数。

Recidivism Rate = (Number of re‑offenders / Total released prisoners) × 100%

再犯率 = (再犯人数 / 释放囚犯总数) × 100%——用于评估刑事司法的改造效果。

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4. Educational Attainment Indicators | 教育成就指标

Education formulas help uncover patterns of inequality by ethnicity, class and gender. The Progress 8 and Attainment 8 systems replaced the old 5 A*–C measure, but the percentage achieving a standard pass in English and maths remains a key headline.

教育公式有助于揭示民族、阶级和性别不平等模式。Progress 8 和 Attainment 8 体系取代了旧式的 5 A*–C 指标，但英语和数学标准达标的百分比仍是关键标题数字。

% Achieving grade 4+ in English and maths = (Pupils achieving 4+ in both / Total pupils at end of KS4) × 100

英语和数学达 4 级及以上的百分比 = (两科均达 4 级及以上学生数 / KS4 结束时学生总数) × 100——4 级被视为标准及格线（9–1 体系中）。

Attainment 8 Score = Sum of points from English (double‑weighted) + Maths (double‑weighted) + 3 EBacc subjects + 3 open subjects

Attainment 8 分数 = 英语（双倍权重）分数 + 数学（双倍权重）分数 + 3 门 EBacc 科目分数 + 3 门开放科目分数的总和——最高分约为 90，是衡量学校平均学术水平的工具。

Progress 8 = (Actual Attainment 8 – Estimated Attainment 8) / 10

Progress 8 = (实际 Attainment 8 – 预估 Attainment 8) / 10——正值表示学生进步超过全国同类基准，负数则表示落后。

Disadvantage gap index = (Average Attainment 8 of non‑disadvantaged – Average Attainment 8 of disadvantaged) / Standard deviation

弱势差距指数 = (非弱势学生平均 Attainment 8 – 弱势学生平均 Attainment 8) / 标准差——量化了社会经济背景对成绩的影响幅度。

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5. Social Stratification Metrics | 社会分层度量公式

Stratification involves quantitative indicators of inequality. While the Gini coefficient is more advanced, GCSE students are expected to use simple proportions and percentages to describe income distribution and relative poverty.

社会分层涉及不平等的量化指标。虽然基尼系数更为高阶，但 GCSE 学生需要运用简单的比例和百分比来描述收入分配和相对贫困。

Relative poverty line (60% of median income) = Median equivalised household income × 0.60

相对贫困线（中位收入的 60%）= 家庭等值化中位收入 × 0.60——低于此线即被视为相对贫困，这是英国官方常用定义。

Poverty rate = (Number of people below the poverty line / Total population) × 100%

贫困率 = (贫困线以下人口数 / 总人口) × 100%——可细分儿童、退休人员等子群体。

Absolute mobility rate = (Number of individuals in a different social class than their parents / Total sample) × 100%

绝对流动率 = (与父母处于不同社会阶级的人数 / 样本总人数) × 100%——反映社会结构为个人提供的机会大小。

Income quintile share = (Total income of the richest 20% / Total income) × 100

五等分收入份额 = (最富 20% 人口的总收入 / 全社会总收入) × 100——用以生动展现财富集中的程度。

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6. Measures of Central Tendency and Spread | 集中趋势与离散程度公式

Researchers use these statistics to summarise data sets. You may be asked to calculate them from a table or to explain why one measure is more appropriate than another.

研究者使用这些统计量概括数据集。考试可能要求你根据表格计算，或解释为何某一指标比另一个更恰当。

Mean = Σx / n (sum of values divided by number of values)

平均数 = Σx / n (所有数值之和除以数值个数)——容易受极端值的影响。

Median = middle value when ordered; if n is even, average of two middle values

中位数 = 排序后居中的数值；若 n 为偶数则为中间两数的平均值——不受极端值干扰，适用于偏态分布。

Mode = most frequently occurring value

众数 = 出现频率最高的数值——特别适用于名义分类数据。

Range = highest value – lowest value

全距 = 最大值 – 最小值——简单却易受异常值影响。

Interquartile Range (IQR) = Q₃ – Q₁ (spread of middle 50%)

四分位距 (IQR) = 第三四分位数 – 第一四分位数 (中间 50% 数据的跨度)——比全距更稳健，常与中位数搭配使用。

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7. Sampling and Percentage Change | 抽样与百分比变化公式

Understanding how samples are drawn and how change is calculated is fundamental for evaluating sociological research. These simple formulas feature in methods questions and mini‑investigations.

理解如何抽取样本以及如何计算变化是评价社会学研究的基础。这些简单公式常出现在方法题和小型调查中。

Sampling fraction = (Sample size) / (Target population size)

抽样比 = 样本量 / 目标总体规模——分数越大，样本代表性通常越好。

Percentage change = [(New value – Old value) / Old value] × 100%

百分比变化 = [(新值 – 旧值) / 旧值] × 100%——用于描述离婚率、犯罪率等随时间的变化。

Response rate = (Number of completed questionnaires / Number issued) × 100%

回收率 = (完成问卷份数 / 发出问卷份数) × 100%——低回收率会削弱研究的代表性。

Sampling error (approximate) = 1 / √(sample size)

抽样误差（近似）= 1 / √(样本量)——样本越大，误差越小；此公式辅助理解置信区间的逻辑。

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8. Key Theorems on Crime and Deviance | 犯罪与越轨核心定理

Sociological ‘theorems’ express causal chains proposed by theorists. They help you structure essays and analyse scenarios by showing how one factor leads to another.

社会学‘定理’表达了理论家提出的因果链条。它们通过展示一个因素如何导向另一个因素，帮助你组织论文和分析场景。

Becker’s Labelling Theorem: Primary deviance + Negative social reaction → Master status → Secondary deviance

贝克标签定理：初级越轨 + 负面社会反应 → 主导身份 → 次级越轨——说明标签如何固化越轨生涯。

Merton’s Strain Theorem: Cultural goals ÷ Legitimate means → Anomie → Innovation/Ritualism/Retreatism/Rebellion

默顿压力定理：文化目标 ÷ 合法手段 → 失范 → 革新/仪式主义/退却/反叛——解释追求美国梦何以催生犯罪。

Cohen’s Status Frustration Theorem: Working‑class boys + Middle‑class measuring rod → Status frustration → Delinquent subculture

科恩地位挫折定理：工人阶级男孩 + 中产阶级衡量标准 → 地位挫折 → 越轨亚文化——指出学校按中产标准评判学生如何引发集体对抗。

Sutherland’s Differential Association Theorem: Excess of definitions favourable to law‑breaking → Criminality

萨瑟兰不同接触定理：赞同违法的定义超过守法定义 → 犯罪倾向——强调学习环境的重要性。

Hirschi’s Social Bond Theorem: Attachment + Commitment + Involvement + Belief = Low delinquency

赫希社会纽带定理：依恋 + 投入 + 参与 + 信念 = 低越轨——控制理论的核心公式。

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9. Key Theorems on Education and Socialisation | 教育与社会化核心定理

Education theorems often contrast functionalist and Marxist accounts of what schools do. Use them to unpack processes such as the hidden curriculum and cultural reproduction.

教育定理常对比功能论和马克思主义对学校作用的解释。用它们来解析隐性课程和文化再生产等过程。

Durkheim’s Social Solidarity Theorem: Transmission of shared norms and values → Social cohesion

涂尔干社会团结定理：共享规范与价值的传递 → 社会凝聚——教育被视为社会的道德粘合剂。

Parsons’ Bridge Theorem: Particularistic standards (family) → Universalistic standards (school) → Value consensus

帕森斯桥梁定理：特殊主义标准（家庭）→ 普遍主义标准（学校）→ 价值共识——学校充当家庭与社会的桥梁。

Bowles and Gintis’ Correspondence Theorem: Hierarchical structure of schooling ↔ Hierarchical structure of work

鲍尔斯与金蒂斯对应定理：学校层级结构 ↔ 工作场所层级结构——教育复制资本主义生产关系。

Bourdieu’s Cultural Capital Theorem: Middle‑class habitus + Dominant cultural capital → Educational advantage

布迪厄文化资本定理：中产阶级惯习 + 主导文化资本 →

Published by TutorHao | Year 10 社会学 Revision Series | aleveler.com

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