📚 Year 10 WJEC Sociology: Formulas & Theorems Quick Reference Guide | Year 10 WJEC 社会学：公式定理速查手册
Welcome to your quick-reference companion for Year 10 WJEC Sociology. Although sociology is a social science built on theories and interpretations, it also relies on precise formulas and principles, especially when analysing data in research methods. This handbook gathers the key calculation formulas you need for your studies, alongside foundational theoretical 'theorems' that sociologists use to explain patterns in society. From calculating the mean of a dataset to applying Weber's multi-dimensional model of stratification, this bilingual guide supports your revision with clarity. Keep it close to master every essential.
欢迎使用 Year 10 WJEC 社会学速查手册。虽然社会学是一门建立在理论与解释之上的社会科学，但它在研究方法中同样依赖于精确的公式与原则——特别是在分析数据时。本手册汇集了你学习所需的关键计算公式，以及社会学家用来解释社会模式的基本理论“定理”。从计算数据集的平均数到应用韦伯的多维分层模型，这份双语指南将用清晰的方式助力你的复习。随时翻阅，掌握每个核心要点。
1. Understanding Key Research Concepts: Variables and Hypotheses | 理解关键研究概念：变量与假设
ationship between an independent variable (IV) and a dependent variable (DV). For example, ‘ cess), and the DV is the outcome (criminal behaviour). The basic formulaic relationship can be expressed as: IV change → DV change.
在社会学研究中，假设是一个可检验的陈述，预测自变量（IV）和因变量（DV）之间的关系。例如，“增加早期教育机会可减少日后的犯罪行为”。自变量是被操控或比较的因素（早期教育机会），因变量是结果（犯罪行为）。其基本公式化关系可表示为：自变量变化 → 因变量变化。
Operationalising variables means turning abstract concepts into measurable forms. For instance, ‘criminal behaviour’ could be operationalised as ‘number of arrests by age 18’. Only then can the hypothesis be tested empirically and a relationship confidently claimed.
操作化变量意味着将抽象概念转化为可测量的形式。例如，“犯罪行为”可操作化为“18岁前被逮捕的次数”。只有如此，假设才能被实证检验，关系才能被确信地确立。
2. Measures of Central Tendency: Mean, Median and Mode | 集中趋势的测量：平均数、中位数与众数
When sociologists analyse quantitative data, they summarise large sets of numbers using measures of central tendency. The three fundamental measures are the mean, median and mode. Each serves a different purpose, especially when handling skewed distributions or outliers.
当社会学家分析定量数据时，他们使用集中趋势的测量来总结大量数字。三个基本测量值是平均数、中位数和众数。它们各有不同用途，尤其在处理偏态分布或异常值时作用明显。
Mean (Arithmetic Average)
The mean is calculated by summing all values and dividing by the total count.
Mean = (x₁ + x₂ + ... + xₙ) / n
平均数（算术平均值）
平均数的计算方式为将所有数值相加，再除以数值的个数。
平均数 = (x₁ + x₂ + ... + xₙ) / n
s on a street: 2, 3, 3, 4, 4, 4, 5, 7. The mean = (2+3+3+4+4+4+5+7)/8 = 32/8 = 4.0 people.
示例：一条街上的家庭人数：2、3、3、4、4、4、5、7。平均数 = (2+3+3+4+4+4+5+7)/8 = 32/8 = 4.0 人。
Median
middle numbers. In the example above, ordered data: 2,3,3,4,4,4,5,7. Median = (4+4)/2 = 4.
中位数
中位数是将数据按顺序排列后位于中间的数值。当数值个数为偶数时，取中间两个数的平均值。在上例中，排序后为：2,3,3,4,4,4,5,7。中位数 = (4+4)/2 = 4。
Mode
The mode is the value that appears most frequently. The dataset above has a mode of 4, as it occurs three times. Some datasets are bimodal (two modes) or have no mode.
众数
众数是出现频率最高的数值。上述数据集的众数是 4，因为它出现了三次。有些数据集是双众数（两个众数）或无众数。
3. Calculating Percentages and Percentage Change | 计算百分比与百分比变化
Percentages express a proportion relative to 100, making it easier to compare groups of different sizes. The core formula is:
Percentage (%) = (Part ÷ Whole) × 100
百分比用于表示相对于100的比例，便于比较不同规模的群体。核心公式为：
百分比(%) = (部分 ÷ 整体) × 100
ents, 200 receive free school meals. The percentage of FSM students = (200/800) × 100 = 25%.
示例：一所学校有800名学生，其中200名享有免费校餐。FSM学生的百分比 = (200/800) × 100 = 25%。
Percentage change measures the relative increase or decrease over time.
Percentage Change = ((New Value - Old Value) ÷ Old Value) × 100
百分比变化衡量随时间变化的相对增加或减少。
百分比变化 = ((新值 - 旧值) ÷ 旧值) × 100
If a town' se from 500 to 650, the percentage change = ((650 - 500)/500) × 100 = (150/500) × 100 = 30% increase.
若某镇的失业人数从500升至650，则百分比变化 = ((650 - 500)/500) × 100 = (150/500) × 100 = 增加30%。
4. Sampling Techniques and the Sampling Fraction | 抽样技术与抽样比
Researchers rarely collect data from every member of a target population. Instead, they draw a sample. The sampling fraction shows what proportion of the population is selected.
Sampling Fraction = Sample Size ÷ Population Size
研究者很少能收集目标总体中每个成员的数据，因此他们抽取样本。抽样比表示被选中的总体比例。
抽样比 = 样本量 ÷ 总体规模
A sampling fraction of 0.05 (or 5%) means that for every 100 people in the population, 5 are included in the sample. A high sampling fraction generally improves representativeness, but the method of selection (e.g. simple random, stratified, quota) is more important for reducing bias.
抽样比0.05（即5%）意味着总体中每100人就有5人被纳入样本。较高的抽样比通常能提高代表性，但选择方法（如简单随机、分层、配额）对于减少偏误更为关键。
5. Sociological Theories: Core Principles as Social Theorems | 社会学理论：作为社会学定理的核心原则
Sociological theories provide overarching explanations for how society functions. Think of these as 'theorems' or general principles that guide sociological analysis. The table below summarises four foundational perspectives.
社会学理论为社会如何运作提供了总体解释。你可以将其视为引导社会学分析的“定理”或一般原则。下表总结了四个基础视角。
| Theory | Core Principle / 'Social Theorem' | 核心原则 / '社会学定理' |
|---|---|---|
| Functionalism | Society is a system of interconnected institutions that work together to maintain stability, value consensus and social order. | 社会是由相互关联的制度组成的系统，这些制度共同作用以维持稳定、价值共识和社会秩序。 |
| Marxism | Society is defined by class conflict between the bourgeoisie (owners) and proletariat (workers). The economic base shapes the superstructure, producing inequality and alienation. | 社会由资产阶级（所有者）与无产阶级（工人）之间的阶级冲突所定义。经济基础决定上层建筑，从而产生不平等与异化。 |
| Feminism | Society is patriarchal; gender inequality is structured into social institutions, and male dominance oppresses women across public and private spheres. | 社会是父权制的；性别不平等被结构化于社会制度中，男性主导在公私领域都对女性构成压迫。 |
| Interactionism | Society is constructed through everyday interactions and the meanings individuals attach to labels, symbols and roles. Behaviour is negotiated, not structurally determined. | 社会通过日常互动以及个体赋予标签、符号和角色的意义而建构。
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