IGCSE Cambridge Sociology: Formulae and Theorems Quick Reference Handbook | IGCSE 剑桥社会学：公式定理速查手册

📚 IGCSE Cambridge Sociology: Formulae and Theorems Quick Reference Handbook | IGCSE 剑桥社会学：公式定理速查手册

This handbook distils the essential ‘formulae’ and ‘theorems’ of IGCSE Cambridge Sociology. Here, ‘formulae’ refer to the key quantitative calculations used in sociological research, while ‘theorems’ denote the foundational theoretical propositions that explain social structures, processes, and inequalities.

本手册提炼了IGCSE剑桥社会学中关键的“公式”与“定理”。此处“公式”指社会学研究中所用的关键定量计算方法，“定理”则指解释社会结构、过程与不平等的基础理论命题。

---

1. Quantitative Calculations in Sociological Research | 社会学研究中的定量计算

Mean: the arithmetic average, calculated as Σx ÷ n, where Σx is the sum of all values and n is the number of values.

平均数：算术平均值，计算公式为 Σx ÷ n，其中 Σx 为所有数值的总和，n 为数值的个数。

Median: the middle value when data are arranged in order. If the number of values is even, it is the average of the two middle values.

中位数：将数据按顺序排列后处于中间位置的数值。若数值个数为偶数，则取中间两个数值的平均数。

Mode: the most frequently occurring value in a data set. A set may have one mode, more than one mode, or no mode at all.

众数：数据集中出现频率最高的数值。一个数据集可能有一个众数、多个众数，或没有众数。

Percentage change = ((New value − Old value) ÷ Old value) × 100%. It measures relative increase or decrease over time.

百分比变化 = ((新值 − 旧值) ÷ 旧值) × 100%。用于测量随时间变化的相对增减幅度。

A rate expresses frequency per defined population, such as crime rate = (number of crimes ÷ total population) × 1,000. It allows comparison across populations of different sizes.

比率表示特定人口中的发生频率，例如犯罪率 = (犯罪数 ÷ 总人口) × 1,000。它使不同规模人口的比较成为可能。

---

2. Sampling Principles: Representativeness and Sampling Error | 抽样原则：代表性与抽样误差

A sample is a subset of a population selected for study. To generalise findings, the sample must be representative of the target population.

样本是从总体中选出用于研究的一个子集。为使研究发现具有普遍性，样本必须对目标总体具有代表性。

Sampling error is the difference between the sample result and the true population value; it decreases as sample size increases.

抽样误差是指样本结果与真实总体值之间的差异；样本容量越大，抽样误差越小。

Random sampling gives every member an equal chance of selection, reducing bias. Stratified sampling divides the population into relevant strata and selects proportionally from each.

随机抽样使每个成员被选中的机会均等，从而减少偏差。分层抽样将总体划分为相关层次，并按比例从各层抽取。

Snowball sampling is used for hard-to-reach groups, where existing participants recruit others. It may lack representativeness but can access hidden populations.

滚雪球抽样用于难以接触的群体，由现有参与者招募其他参与者。它可能缺乏代表性，但能接触到隐蔽群体。

---

3. Measuring Inequality: Gini Coefficient and Lorenz Curve | 不平等测量：基尼系数与洛伦兹曲线

The Gini coefficient is derived from the Lorenz curve, which plots cumulative income share against cumulative population share. Gini = A ÷ (A + B), where A is the area between the line of perfect equality and the Lorenz curve, and B is the area under the Lorenz curve.

基尼系数源自洛伦兹曲线，该曲线描绘累计人口份额与累计收入份额之间的关系。基尼系数 = A ÷ (A + B)，其中 A 为绝对平等线与洛伦兹曲线之间的面积，B 为洛伦兹曲线下方的面积。

A Gini coefficient of 0 represents perfect equality; 1 represents perfect inequality. The higher the coefficient, the greater the inequality.

基尼系数为 0 表示完全平等，1 表示完全不平等。系数越高，不平等程度越大。

The quintile share ratio compares the income of the richest 20% to the poorest 20%. A higher ratio signals more inequality.

五等分份额比率比较最富有的 20% 与最贫穷的 20% 人口的收入。比率越高，不平等越严重。

---

4. Functionalism: Organic Analogy and Social Order | 功能主义：有机体类比与社会秩序

Functionalism views society as a system of interconnected parts that work together to maintain stability and equilibrium, much like a biological organism (Durkheim, Parsons).

功能主义将社会视为一个由相互关联的部分组成的系统，各部分协同运作以维持稳定与均衡，类似于生物有机体（Durkheim, Parsons）。

Social institutions (family, education, religion) perform essential functions: manifest functions are intended and recognized, latent functions are unintended but still contribute to social stability (Merton).

社会制度（家庭、教育、宗教）发挥着基本功能：显性功能是有意且被认可的功能，隐性功能虽非有意但仍有助于社会稳定（Merton）。

Value consensus – shared norms and values – is the glue that holds society together. Anomie occurs when norms break down, leading to social disorder (Durkheim).

价值共识——共享的规范与价值观——是维系社会的粘合剂。当规范瓦解时便会出现失范，导致社会失序（Durkheim）。

Critics argue functionalism overlooks conflict,

Published by TutorHao | IGCSE 社会学 Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）