📚 Year 9 Cambridge Sociology: Formula & Theorem Quick Reference Handbook | Year 9 剑桥社会学：公式定理速查手册
In Year 9 Cambridge Sociology, understanding key 'formulae' and 'theorems' helps you decode social patterns and research data. While sociology is not a mathematical science, certain statistical tools and theoretical principles function like formulae that explain human behaviour. This handbook summarises essential calculation methods and major sociological theorems, providing a quick reference for revision.
在Year 9剑桥社会学课程中，理解关键的 "公式" 与 "定理" 有助于解读社会模式和研究数据。虽然社会学不是数学科学，但某些统计工具和理论原理可以像公式一样解释人类行为。本手册汇总了必要的计算方法和主要社会学定理，为复习提供速查参考。
1. Understanding Formulae in Sociology | 理解社会学中的公式
Sociologists use quantitative tools to analyse society. These 'formulae' include measures of central tendency, percentages, and rates. They are not physical laws but reliable tools for describing social facts. Understanding how to calculate and interpret them is a core skill for Cambridge Sociology.
社会学家使用量化工具分析社会。这些 "公式" 包括集中趋势测量、百分比和比率。它们不是物理定律，但却是描述社会事实的可靠工具。掌握如何计算和解读它们是剑桥社会学的核心技能。
2. Mean, Median, Mode | 平均数、中位数和众数
The mean is the arithmetic average. It is calculated by summing all values and dividing by the number of cases.
平均数是算术平均值，由所有数值之和除以案例数计算得出。
Mean = Σx ÷ n
The median is the middle value when data are arranged in order. If there are two middle values, take their average.
中位数是将数据按序排列后的中间值。如果中间有两个数值，则取它们的平均值。
The mode is the most frequently occurring value in a dataset. A dataset can have one mode (unimodal), two (bimodal), or more.
众数是数据集中出现次数最多的值。一个数据集可能有一个众数（单峰）、两个（双峰）或更多。
3+5+5+7+8+9) ÷ 7 = 39 ÷ 7 ≈ 5.57; Median = 5 (the middle value); Mode = 5 (appears twice).
示例：数值 2, 3, 5, 5, 7, 8, 9：平均数 = (2+3+5+5+7+8+9) ÷ 7 = 39 ÷ 7 ≈ 5.57；中位数 = 5（中间值）；众数 = 5（出现两次）。
3. Percentage Change | 百分比变化
Percentage change shows the relative increase or decrease between an old value and a new value. It is widely used to analyse trends in crime rates, educational attainment, and other social indicators.
百分比变化显示旧值与新值之间的相对增加或减少。它广泛用于分析犯罪率、教育程度等社会指标的趋势。
Percentage change = [(New value − Original value) ÷ Original value] × 100
, if exam pass rate rose from 70 to 77, the percentage change is [(77−70) ÷ 70] × 100 = 10% increase.
如果结果为正，表明增加；为负则表明减少。例如，考试通过率从70%上升到77%，百分比变化为 [(77−70) ÷ 70] × 100 = 10% 增加。
4. Rate Calculations (Birth, Death, Crime) | 比率计算（出生率、死亡率、犯罪率）
Rates allow sociologists to compare frequencies across different populations. The basic formula is:
比率让社会学家能够比较不同人群中的发生频率。基本公式为：
Rate = (Number of events ÷ Total population) × 1,000
records 200 crimes, the crime rate is (200 ÷ 50,000) × 1,000 = 4 crimes per 1,000 people.
乘数（通常为1,000）将比率标准化为每千人的数值。例如，如果一个5万人口的城市记录了200起犯罪，犯罪率为 (200 ÷ 50,000) × 1,000 = 每千人4起犯罪。
× 1,000. Death rate uses the same logic. These help demographers study population change.
出生率 = (活产婴儿数 ÷
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