Year 11 CIE Sociology: Formulas and Theorems Quick Reference | 剑桥IGCSE社会学：公式定理速查手册

📚 Year 11 CIE Sociology: Formulas and Theorems Quick Reference | 剑桥IGCSE社会学：公式定理速查手册

Welcome to your essential quick reference for Year 11 CIE Sociology. Here we distil the most important quantitative formulas used in sociological research and the core theoretical ‘theorems’ proposed by key sociologists. Whether you are calculating demographic rates or applying Marxist theory, this guide gives you the tools to revise efficiently.

欢迎使用这本Year 11剑桥IGCSE社会学必备速查手册。我们提炼了社会学研究中最重要的量化公式，以及关键社会学家提出的核心理论“定理”。无论你是在计算人口比率还是运用马克思主义理论，这本指南都将为你提供高效复习的工具。

1. Key Demographic Formulas | 重要人口统计公式

The crude birth rate measures the number of live births per 1,000 population in a given year. This basic formula is widely used to compare fertility across societies.

粗出生率衡量每千人中一年的活产数，是用于跨社会生育率比较的基本公式。

Crude Birth Rate (CBR) = (Total live births ÷ Total mid-year population) × 1000

Similarly, the crude death rate captures mortality and helps demographers understand population decline.

类似地，粗死亡率反映死亡水平，帮助人口学家理解人口减少情况。

Crude Death Rate (CDR) = (Total deaths ÷ Total mid-year population) × 1000

Natural increase (or decrease) is simply the difference between the birth and death rates, often expressed per 1,000.

自然增长率（或减少）即出生率与死亡率之差，通常也以每千人表示。

Natural Increase = CBR − CDR

The infant mortality rate is a sensitive indicator of a country’s health and development, calculated as deaths of infants under one year per 1,000 live births.

婴儿死亡率是衡量国家健康和发展水平的敏感指标，即每千名活产中未满周岁死亡的婴儿数。

Infant Mortality Rate = (Deaths under age 1 ÷ Live births) × 1000

Net migration rate reveals whether a society gains or loses people through migration.

净迁移率反映一个社会因迁移而净增加或减少的人口。

Net Migration Rate = (Immigrants − Emigrants) ÷ Total population × 1000

Sociologists also compute the divorce rate as the number of divorces per 1,000 married couples, though some use per 1,000 total population.

社会学家计算离婚率时，通常用每千对已婚夫妇的离婚对数，有时也用每千人中的离婚数。

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

2. Measures of Social Inequality | 社会不平等测量

Social inequality is often captured by the Gini coefficient, a statistical measure of income or wealth distribution within a society.

社会不平等通常用基尼系数来衡量，它是对社会内部收入或财富分配状况的统计量度。

Gini Coefficient = A ÷ (A + B)

where A is the area between the Lorenz curve and the line of perfect equality, and B is the area under the Lorenz curve. The result ranges from 0 (perfect equality) to 1 (perfect inequality).

其中A是洛伦兹曲线与完全平等线之间的面积，B是洛伦兹曲线下的面积。结果介于0（完全平等）与1（完全不平等）之间。

The Lorenz curve visually represents cumulative income shares against cumulative population shares, with the 45-degree line representing perfect equality.

洛伦兹曲线直观展示累积收入份额与累积人口份额的关系，45度对角线代表完全平等。

Another common indicator is the quintile ratio, which divides the income share of the top 20% by that of the bottom 20%, revealing how many times richer the richest group is.

另一种常用指标是五分位比，即最高20%人口的收入份额除以最低20%人口的收入份额，显示最富群体的

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