📚 Year 11 OCR Sociology: Quick-reference Formulas & Theorems | 公式定理速查手册
This handbook provides a compact revision tool for Year 11 OCR Sociology students, covering essential research methods formulas, key theoretical 'theorems' expressed as sociological equations, and quick-reference definitions. Use it alongside your course notes to reinforce command of the terminology and numerical skills required for the exam.
本手册为 Year 11 OCR 社会学学生提供精简的复习工具，涵盖研究方法的必背公式、用社会学方程式表达的关键理论“定理”，以及速查定义。配合课堂笔记使用，能帮助你巩固术语和考试所需的计算技能。
1. Sampling Frame & Sample Size Formula | 抽样框与样本量公式
Understanding how to select a representative sample is fundamental. The sampling frame is the list from which the sample is drawn. While there is no fixed universal formula for sample size in GCSE-level sociology, a useful guideline is to ensure the sample is large enough to reflect the target population's diversity.
理解如何选择具有代表性的样本是基础。抽样框是抽取样本的名单。虽然 GCSE 社会学中没有固定的通用样本量公式，但一条实用的指导原则是确保样本足够大，以反映目标总体的多样性。
r statistical analysis; however, representativeness also depends on sampling technique and response rate.
基本样本量指导原则：进行统计分析时 n ≥ 30；但代表性也取决于抽样技术和回收率。
Response Rate = (Number of completed responses ÷ Number of invitations) × 100%
| Simple random sampling | Each member has equal chance of selection; minimizes bias but needs a full sampling frame. | 简单随机抽样：每个成员被选中的机会均等；偏差最小但需要完整抽样框。 |
| Stratified sampling | ch. Formula: sample per stratum = (stratum size ÷ total population) × desired sample size. | 分层抽样：将总体分为层（如年龄段），从各层随机抽样。公式：每层样本量 = (层规模 ÷ 总体规模) × 所需样本量。 |
| Systematic sampling | very kth person; k = population size ÷ sample size. Example: 1000 people, need 100 → k=10. | 系统抽样：每隔 k 人抽取一人；k = 总体规模 ÷ 样本量。例如：1000 人，需 100 → k=10。 |
2. Measures of Central Tendency | 集中趋势测量公式
Sociologists often summarise quantitative data using averages. The three measures of central tendency must be known for exam calculations.
社会学家常用平均数来概括量化数据。考试中必须掌握三种集中趋势的测量方法。
Mean = Σx / n
The mean is the sum of all values (Σx) divided by the number of values (n). It uses all data but is affected by extreme outliers.
算术平均数是所有数值之和 (Σx) 除以数值个数 (n)。它利用了全部数据，但易受极端异常值影响。
Median = middle value when data is ordered
If the number of values is odd, the median is the central number. If even, it is the mean of the two middle numbers. The median is not distorted by outliers.
若数值个数为奇数，中位数是中间那个数；若为偶数，则是中间两数的平均值。中位数不受异常值干扰。
Mode = most frequently occurring value
The mode is the only measure suitable for nominal (categorical) data. A dataset can have more than one mode.
众数是出现频率最高的值。它是唯一适用于名义（分类）数据的集中趋势指标。数据集可以有多个众数。
3. Measures of Dispersion | 离散程度测量公式
Dispersion tells us how spread out the data are. The simplest measure is the range; a more advanced concept (useful for evaluation) is standard deviation, though GCSE calculation may not be required.
离散程度反映数据的分散情况。最简单的指标是全距（极差）；更高级的概念是标准差（有助于评估），但 GCSE 可能不要求计算。
Range = Highest value – Lowest value
The range is quick to calculate but only uses two extreme values, so it can be misleading if there are outliers.
全距计算简便，但只用到两个极端值，因此存在异常值时会误导。
Interquartile range (IQR) = Q3 – Q1 (the range of the middle 50%). Use for skewed data.
四分位距 (IQR) = Q3 – Q1（中间 50% 数据的范围）。适用于偏态数据。
Standard deviation (σ) = √[ Σ(x − x̄)² / n ]
Standard deviation measures the average distance of each data point from the mean. A low SD indicates data are clustered around the mean; a high SD shows wide spread. Its unit is the same as the data.
标准差衡量各数据点与平均值的平均距离。低标准差表示数据聚集在平均值周围；高标准差表示分布广泛。其单位与数据一致。
4. The Socialisation Equation | 社会化公式
Sociologists explain how individuals learn the norms and values of society. A simple 'equation' helps remember the agents of socialisation.
社会学家解释个体如何学习社会规范与价值观。一个简单的“方程式”有助于记忆社会化的主体。
lisation (family) + Secondary Socialisation (education, media, peers, religion, workplace)
Primary socialisation occurs in early childhood within the family, where basic language, norms, and values are internalised. Secondary socialisation continues throughout life as we encounter new social contexts.
初级社会化发生在儿童早期家庭中，内化基本的语言、规范与价值观。次级社会化贯穿一生，当人们接触新的社会情境时发生。
- Family: first norms, gender roles, emotional bonds
- 家庭：最初的规范、性别角色、情感纽带
- Education: formal curriculum and hidden curriculum
- 教育：正式课程与隐性课程
- Media: transmits stereotypes, consumer culture
- 媒体：传递刻板印象、消费文化
- Peers: influence tastes, slang, independence from adults
- 同伴：影响品味、俚语、脱离成人的独立性
5. Social Stratification Formulas | 社会分层公式
Social stratification refers to the way society is layered in a hierarchy. Key concepts can be expressed as relational statements regarding class, status, and power.
社会分层指社会按等级分层的方式。核心概念可以用关于阶级、地位和权力的关系式来表达。
Socio-economic status (SES) = Income + Education + Occupation
Weber’s multi-dimensional view of stratification includes class (economic), status (social prestige), and party (political power). Marx focused on a binary relation.
韦伯的多维分层观包括阶级（经济）、地位（社会声望）和政党（政治权力）。马克思则侧重于二元关系。
: Bourgeoisie (own means of production) + Proletariat (sell labour power) → Class conflict
Bourgeoisie exploit the proletariat by extracting surplus value. This conflict is the engine of historical change, leading eventually to revolution.
资产阶级通过榨取剩余价值剥削无产阶级。这一冲突是历史变革的动力，最终导致革命。
Life chances = access to resources such as healthcare, education, housing, leisure
Life chances are a Weberian concept that describes the opportunities people have to improve their quality of life; they are strongly shaped by social class.
生活机会是韦伯式的概念，描述人们提高生活质量的机会；这些机会深受社会阶级的影响。
6. Theoretical Perspectives: Quick-Reference 'Theorems' | 理论视角速查“定理”
Each major sociological perspective can be summarised with a core proposition, acting like a theorem about society.
每一个主要社会学视角都可以用一条核心命题来概括，就像关于社会的定理一样。
Functionalism: Society is a system of interconnected parts (institutions) that work together to maintain stability. Durkheim: Society > sum of individuals.
功能主义：社会是一个由相互关联的部分（制度）组成的系统，各部分协同工作以维持稳定。涂尔干：社会大于个体之和。
Marxism: The economic base (infrastructure) determines the superstructure (politics, law, culture). All institutions serve ruling class interests.
马克思主义：经济基础（下层建筑）决定上层建筑（政治、法律、文化）。一切制度服务于统治阶级的利益。
Feminism: Society is patriarchal – structured by male dominance. Gender inequality is systemic, not natural. Liberal, Marxist, and radical feminists all agree on the problem but differ on solutions.
女权主义：社会是父权制的——由男性主导所建构。性别不平等是系统性的，而非自然的。自由派、马克思主义和激进女权主义者都认同这一问题，但对解决方案看法不同。
Interactionism: Society is constructed through everyday social interaction and the meanings people attach to actions. Labelling theory is a classic example.
互动论：社会通过日常社会互动及人们赋予行动的意义而建构。标签理论是经典例子。
7. Education & Social Mobility Formula | 教育与社会流动公式
Sociologists study how education influences social mobility. The achievement gap can be linked to cultural and material factors.
社会学家研究教育如何影响社会流动。成就差距可以关联到文化因素和物质因素。
Cultural capital (Bourdieu) + Material capital → Educational attainment
Cultural capital includes knowledge, language, and attitudes valued by the education system. Middle-class children often possess more cultural capital, giving them an advantage.
文化资本包括教育系统所重视的知识、语言和态度。中产阶级儿童通常拥有更多文化资本，从而占据优势。
Material deprivation formula:
物质剥夺公式：
+ Low income + Inadequate diet → Lower attendance, lower concentration → Lower achievement
Material factors directly affect a child's ability to learn. Government statistics consistently show a strong link between free school meal eligibility and GCSE performance.
物质因素直接影响儿童的学习能力。官方统计一贯显示，免费校餐资格与 GCSE 成绩之间存在强相关。
Social mobility types:
社会流动类型：
- Intergenerational mobility: change in status between parents and children
- 代际流动：父母与子女之间地位的变化
- Intragenerational mobility: change in status within a person's own lifetime
- 代内流动：个人一生中地位的变化
8. Crime & Deviance: Theory Equations | 犯罪与偏差行为理论公式
Deviance is behaviour that breaks social norms; crime breaks formal laws. Explanations can be structured as theoretical equations.
偏差行为是违反社会规范的行为；犯罪则是违反正式法律。相关解释可以结构化为理论公式。
Merton's Strain Theory: Cultural goals + Blocked legitimate means → Anomie → Deviance
When society sets universally high goals (e.g. wealth) but fails to provide equal legitimate opportunities, a strain is created. Individuals adapt in five ways: conformity, innovation, ritualism, retreatism, rebellion.
当社会设定全民皆高的目标（如财富）却未能提供平等的合法机会时，便产生压力。个体以五种方式适应：遵从、创新、仪式主义、退缩、反叛。
Becker's Labelling Theory: Deviance is not a quality of the act but a consequence of the label applied.
An act only becomes deviant when powerful groups successfully label it as such. The label can lead to a self-fulfilling prophecy and a deviant career.
一个行为只有在强势群体成功将其贴上偏差标签时才会成为偏差。标签可能导致自证预言与偏差生涯。
Official crime statistics formula:
官方犯罪统计公式：
Recorded crime = Reported crime × Police recording practices
The dark figure of crime refers to unreported and unrecorded crime. Victim surveys (CSEW) reveal a much higher crime rate than police figures.
犯罪黑数指未被报告和未被记录的犯罪。受害调查 (CSEW) 显示的犯罪率远高于警方数据。
9. Research Ethics Quick-Reference | 研究伦理速查
Ethical considerations are as important as methodological ones in sociological research. Memorising the BSA (British Sociological Association) principles can be done through a simple checklist.
在社会学研究中，伦理考量与方法论考量同等重要。记住英国社会学协会 (BSA) 的原则，可以用一份简明的清单。
Ethical principles formula:
伦理原则公式：
iality + Avoidance of harm + Right to withdraw + Deception minimisation → Ethical research
- Informed consent: participants must know the aim and procedures, and agree voluntarily.
- 知情同意：参与者必须了解目的与流程并自愿同意。
- Confidentiality: data must be anonymised; real names not used.
- 保密：数据须匿名化；不使用真名。
- Physical/psychological harm must be avoided; sensitive topics need extra care.
- 必须避免身体/心理伤害；敏感话题需格外谨慎。
- Participants have the right to withdraw at any stage without penalty.
- 参与者有权在任何阶段退出而不受处罚。
- Deception should be minimal and justified; debriefing is required if deception occurs.
- 欺骗应尽量减少并说明理由；若存在欺骗，事后须进行情况说明。
10. Key Sociologists & Theories Speed Check | 关键社会学家与理论速查
Associate each key thinker with their core contribution – like a theorem referencing system. This helps in writing essays where you need to apply named studies.
将每位关键思想家与其核心贡献联系起来——就像定理引用系统。这有助于你在需要引用具名研究的论文中灵活运用。
| Émile Durkheim | Functionalism, anomie, study of suicide as a social fact | 功能主义、失范、将自杀作为社会事实研究 |
| Karl Marx | Class conflict, bourgeoisie vs. proletariat, alienation | 阶级冲突、资产阶级与无产阶级、异化 |
| Max Weber | Verstehen (empathetic understanding), social action, bureaucratic rationality | 理解、社会行动、官僚制理性 |
| Pierre Bourdieu | Cultural, social, and economic capital; habitus | 文化、社会和经济资本；惯习 |
| Ann Oakley | Feminist research on housework, gender socialisation | 女权主义家务劳动研究、性别社会化 |
| Howard Becker | Labelling theory, moral entrepreneurs | 标签理论、道德企业家 |
| Robert K. Merton | Strain theory, manifest and latent functions | 紧张理论、显性与隐性功能 |
11. Data Analysis Quick Formulas | 数据分析速用公式
Interpreting tables and graphs is a required skill. Convert raw numbers into percentages for comparisons; use totals to check consistency.
解读表格和图表是必备技能。将原始数据转换为百分比以便比较；使用总数检查一致性。
Percentage = (Part ÷ Whole) × 100%
Example: if 45 out of 300 respondents agree, percentage = (45 ÷ 300) × 100% = 15%.
例如：300 名受访者中 45 人同意，百分比 = (45 ÷ 300) × 100% = 15%。
Percentage change:
百分比变化：
% change = [(New value – Old value) ÷ Old value] × 100%
This is vital for analysing trends over time, e.g. changes in divorce rates or exam results.
这对分析时间趋势至关重要，如离婚率或考试成绩的变化。
Ratio: tities, e.g. the dependency ratio = (number of dependants ÷ working-age population) × 100.
比率：表示两个数量之间的关系，例如抚养比 = (受抚养人口 ÷ 劳动年龄人口) × 100。
12. Exam Technique 'Formulas' for Answers | 答题技巧“公式”
Structuring exam answers can also be approached with a simple formula. For OCR's extended responses, follow the PEEL or PEA structure.
架构考试答案也可以运用简单的公式。对于 OCR 的扩展回答，可遵循 PEEL 或 PEA 结构。
PEEL: Point + Evidence + Explanation + Link
- Point: a clear sentence stating your argument
- 论点：一句清晰陈述你观点的句子
- Evidence: a study, statistic, or key concept (name the sociologist)
- 证据：一项研究、统计数据或关键概念（注明社会学家）
- Explanation: why the evidence supports your point; show sociological reasoning
- 解释：说明证据为何支持你的论点；展现社会学推理
- Link: connect back to the question or to the next paragraph
- 回扣：回扣题目或过渡到下一段
For 4-mark 'define' questions: precise definition + example.
4 分“定义”题：精确定义 + 例子。
For 12-mark discussion: present two sides, use at least two perspectives, end with a justified conclusion.
12 分论述题：呈现正反两面，至少使用两个视角，以有理有据的结论收尾。
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