📚 IGCSE CAIE Sociology: Formula & Theorem Quick Reference Handbook | IGCSE CAIE 社会学：公式定理速查手册
This handbook compiles essential quantitative formulas and key theoretical theorems for the IGCSE CAIE Sociology syllabus. Use it as a rapid revision tool to master the calculations behind demographic trends, inequality measures, and research methods, as well as the core propositions that shape sociological perspectives.
本手册汇编了 IGCSE CAIE 社会学大纲中核心的量化公式与关键理论命题。你可将它用作快速复习工具，掌握人口趋势、不平等测量和研究方法背后的计算，以及塑造社会学视角的核心主张。
1. Demographic Rates and Population Change | 人口统计率与人口变化
The Crude Birth Rate (CBR) measures the number of live births per 1,000 people in a population per year. It is one of the simplest demographic indicators for comparing fertility across societies.
粗出生率 (CBR) 衡量每年每千人口中的活产婴儿数。它是比较不同社会生育率的最简单人口指标之一。
CBR = (Number of live births / Total mid-year population) × 1000
The Crude Death Rate (CDR) captures the number of deaths per 1,000 individuals annually. A falling CDR often accompanies improvements in healthcare and nutrition during demographic transition.
粗死亡率 (CDR) 反映每年每千人口中的死亡人数。在人口转型过程中，死亡率的下降通常伴随医疗保健和营养的改善。
CDR = (Number of deaths / Total mid-year population) × 1000
The Rate of Natural Increase is found by subtracting the CDR from the CBR. It indicates the pace of organic population growth, excluding migration, and can be positive, negative, or zero.
自然增长率由粗出生率减去粗死亡率得出。它反映了排除迁移后的人口自然增长速度，可以为正、负或零。
Natural Increase Rate = CBR − CDR (expressed per 1000)
2. Migration and Net Migration Rate | 迁移与净迁移率
Net migration rate accounts for the difference between immigrants and emigrants per 1,000 population. It is crucial for understanding population change in areas affected by push and pull factors.
净迁移率计算每千人口中迁入者与迁出者的差额。对于理解受推拉因素影响的地区人口变化至关重要。
Net Migration Rate = ((Immigrants − Emigrants) / Total mid-year population) × 1000
A positive value signals net in-migration, which can expand the labour force but may strain public services. A negative value indicates net out-migration, often linked to economic decline or conflict.
正数值表示净迁入，可能扩大劳动力但给公共服务带来压力。负数值表示净迁出，常与经济衰退或冲突相关。
3. Dependency Ratio and Economic Burden | 抚养比与经济负担
The Age Dependency Ratio expresses the number of dependants (young and old) relative to the working-age population. It is a key measure of the economic pressure on the productive sector.
年龄抚养比表示受抚养人口（幼年和老年）相对于劳动适龄人口的数量。它是衡量生产部门经济压力的关键指标。
Age Dependency Ratio = ((Pop₀₋₁₄ + Pop₆₅₊) / Pop₁₅₋₆₄) × 100
A ratio above 60% is commonly seen in ageing societies where pension and healthcare costs rise. Policymakers use this formula to plan schools, pensions, and immigration policies.
抚养比超过60%通常出现在老龄化社会，伴随养老金和医疗成本上升。政策制定者利用该公式规划学校、养老金和移民政策。
4. Crime Rate and Deviance Measurement | 犯罪率与越轨测量
The official crime rate is standardised per 100,000 population to allow comparisons across regions and over time. It relies on recorded crimes, which may underrepresent actual deviance due to the dark figure of crime.
官方犯罪率按每十万人标准化，便于跨地区和时间比较。它依赖记录在案的犯罪，可能因犯罪暗数而低估真实越轨行为。
Crime Rate = (Number of recorded crimes / Total population) × 100,000
Sociologists also track specific offence rates, such as violent crime rate or property crime rate, using the same denominator. This helps evaluate social control and the effectiveness of policing.
社会学家还以同样分母跟踪暴力犯罪率或财产犯罪率等具体犯罪率。这有助于评估社会控制与警务效果。
5. Divorce Rate and Family Instability | 离婚率与家庭不稳定性
The crude divorce rate measures the number of divorces per 1,000 people in a given year. It is a broad indicator of family instability, though it does not account for the married population directly.
粗离婚率衡量某年每千人口中的离婚对数。这是家庭不稳定性的粗略指标，尽管它没有直接考虑已婚人口基数。
Crude Divorce Rate = (Number of divorces in a year / Total mid-year population) × 1000
To refine the measure, some sociologists calculate the divorce rate per 1,000 married couples, which gives a clearer picture of the risk of divorce within marriages.
为细化测量，一些社会学家计算每千对已婚夫妇的离婚率，从而更清晰地反映婚姻内部的离婚风险。
6. Unemployment Rate and Labour Force | 失业率与劳动力
The unemployment rate captures the proportion of the labour force that is actively seeking work but unable to find it. The labour force itself consists of employed plus unemployed individuals of working age.
失业率反映劳动力中积极求职但无法找到工作的比例。劳动力本身由适龄的就业者与失业者构成。
Unemployment Rate = (Number of unemployed / Labour force) × 100
The labour force participation rate shows what percentage of the working-age population is economically active. It highlights gender gaps and structural changes in employment.
劳动力参与率显示适龄劳动人口中从事经济活动的比例。它突显性别差距和就业的结构性变化。
Labour Force Participation Rate = (Labour force / Working-age population) × 100
7. Measures of Central Tendency | 集中趋势的测量
The mean is the arithmetic average, computed by summing all values and dividing by the number of cases. It is sensitive to outliers and widely used in survey analysis.
均值是算术平均数，通过求和除以个案数得出。它对极端值敏感，广泛用于调查分析。
Mean = Σx / n
The median is the middle value when data are ordered. It is less affected by extreme scores and is preferred when reporting income distributions or central tendency in skewed data.
中位数是数据排序后的中间值。它较少受极端值影响，在报告收入分布或偏态数据集中趋势时更受青睐。
The mode is the most frequently occurring value. It can be used with nominal data such as religious affiliation or marital status.
众数是出现频率最高的值。它可用于宗教信仰或婚姻状况等名义数据。
8. Measures of Dispersion | 离散程度的测量
The range is the simplest measure of spread, calculated as the difference between the maximum and minimum values. It gives a quick sense of data spread but ignores the distribution shape.
极差是最简单的离散度量，由最大值减去最小值求得。它快速体现数据跨度，但忽略分布形态。
Range = Xₘₐₓ − Xₘᵢₙ
The interquartile range (IQR) is the difference between the upper quartile (Q3) and the lower quartile (Q1). It focuses on the middle 50% of data and is robust against outliers.
四分位距 (IQR) 是上四分位数 (Q3) 与下四分位数 (Q1) 之差。它聚焦数据的中间50%，对异常值稳健。
IQR = Q3 − Q1
9. Sampling and Error in Social Research | 社会研究中的抽样与误差
The sampling fraction indicates the proportion of the target population selected for a study. A larger fraction reduces sampling error but increases cost and effort.
抽样分数表示目标人群中被选中参与研究的比例。分数越大，抽样误差越小，但成本和精力增加。
Sampling fraction = n / N
Sampling error is the discrepancy between a sample statistic and the true population parameter. It is inevitable in random sampling, but its size can be estimated using the standard error formula.
抽样误差是样本统计量与总体参数真实值之间的差异。它在随机抽样中不可避免，但其大小可通过标准误公式估算。
To improve representativeness, sociologists combine stratified sampling with a known sampling fraction for each subgroup. This ensures that minority groups are adequately represented.
为提高代表性，社会学家将分层抽样与各子群体的已知抽样分数结合使用。这确保少数群体被充分代表。
10. Key Theoretical Theorems in Sociology | 社会学核心理论定理
Durkheim's Anomie Theorem: Anomie arises when rapid social change weakens normative regulation, causing a breakdown in shared values. High anomie can lead to increased deviance and even suicide.
涂尔干的失范定理：当急剧的社会变迁弱化规范调节时，便出现失范，导致共享价值崩溃。高度失范可引发越轨行为增多，甚至自杀率上升。
Marx's Immiseration Thesis: Under capitalism, the bourgeoisie extracts surplus value, leading to the progressive impoverishment of the proletariat. This polarisation of classes fuels revolutionary consciousness.
马克思的贫困化命题：在资本主义下，资产阶级榨取剩余价值，导致无产阶级日益贫困。这种阶级两极分化催生革命意识。
Davis and Moore's Functionalist Stratification Theorem: Social inequality is functionally necessary to ensure that the most talented individuals fill the most important positions. High rewards motivate training and effort.
戴维斯和摩尔的功能主义分层定理：社会不平等在功能上是必要的，以确保最有才能的个体担任最重要的职位。高回报激励培训与努力。
Becker's Labelling Theorem: Deviance is not inherent in an act but is created by the social reaction and labels applied by others. Once labelled, individuals may embrace a deviant career through self-fulfilling prophecy.
贝克尔的标签定理：越轨并非行为固有，而是由社会反应与他人贴上的标签所创造。一旦被标签，个体可能通过自我实现预言走向越轨生涯。
Parsons' Functional Fit Theorem: The nuclear family emerges to fit the needs of an industrial society requiring geographical mobility and specialised roles. Extended kinship ties weaken as structural differentiation increases.
帕森斯的功能适应定理：核心家庭的出现是为了适应工业社会对地理流动性和专门化角色的需求。随着结构分化加剧，扩展亲属纽带减弱。
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