📚 Year 11 Edexcel Sociology: Quick Reference Guide to Formulas and Theorems | Year 11 Edexcel 社会学：公式定理速查手册
Sociology is often perceived as a purely qualitative subject, but mastering quantitative techniques is crucial for analysing social trends and research data in the Edexcel GCSE course. This quick reference handbook distills all the essential statistical formulas you need - from calculating the mean to interpreting crime rates - alongside pivotal sociological theorems that explain patterns of inequality, deviance and social order. Keep this guide close during revision to quickly recall methods and theories under exam pressure.
社会学常被视为纯定性学科，但掌握定量技术对于分析社会趋势与研究数据在爱德思 GCSE 课程中至关重要。本速查手册浓缩了你所需的全部基本统计公式——从计算均值到解释犯罪率——并同时梳理了解释不平等、越轨与社会秩序模式的关键社会学定理。请把本指南放在手边，在备考压力下快速回顾方法与理论。
1. Mean, Median and Mode: Measures of Central Tendency | 均值、中位数与众数：集中趋势的测量
In sociological research, measures of central tendency summarise a whole distribution with a single number, so that large data sets - such as the average weekly income of 2,000 households - become easier to compare and describe. The mean is the arithmetic average: add every value and divide by the number of cases. It uses every piece of data, which makes it the most informative measure, but it is easily distorted by extreme values (outliers), such as one very high earner inside a sample of ordinary families. The median is the middle value once the data has been ranked in order; with an even number of cases, take the halfway point between the two central values. The mode is the value that occurs most frequently, and it is the only measure of central tendency that works with nominal categories such as religion, ethnicity or favourite newspaper.
在社会学研究中，集中趋势的测量用单一数字概括整个分布，使庞大的数据集——例如 2,000 个家庭的周收入平均值——更容易比较与描述。均值是算术平均数：把所有数值相加，再除以案例数。它利用了每一个数据，因此信息量最大，但极易被极端值（离群值）扭曲，例如一群普通家庭样本里出现一位收入极高者。中位数是把数据按顺序排列后的中间值；当案例数为偶数时，取中间两个数值的中点。众数是出现频率最高的数值，也是唯一能用于定类类别（如宗教、族裔或最常阅读的报纸）的集中趋势测量。
Mean = Σx ÷ n | Median position = (n + 1) ÷ 2 | Mode = the most frequent value
. The mean is 44 ÷ 6 ≈ 7.3 hours; the median is (6 + 7) ÷ 2 = 6.5 hours; the mode is 6 hours. Because the mean is pulled upwards by the value 12, the median gives a fairer picture of the typical student' orking week - a point examiners like to see discussed when evaluating official statistics.
一个实例可以清楚说明差异。某社会学班收集了六名学生每周有偿工作的小时数：4、6、6、7、9 和 12。均值为 44 ÷ 6 ≈ 7.3 小时；中位数为 (6 + 7) ÷ 2 = 6.5 小时；众数为 6 小时。由于均值被数值 12 向上拉动，中位数更能公平地反映"典型"学生的每周工作时长——在评价官方统计时，考官很喜欢看到这一点的讨论。
2. Range, Standard Deviation and Dispersion | 极差、标准差与离散程度
Two distributions can share exactly the same mean yet look completely different. Measures of dispersion describe how spread out the data is. The range is the simplest measure: the highest value minus the lowest value. It is quick to calculate, but it depends on only two cases, so a single outlier destroys it. The interquartile range - the range covered by the middle 50% of cases - is far more robust. Standard deviation is the most powerful measure: it expresses the average distance of each case from the mean, so a small standard deviation means the data cluster tightly around the mean, while a large one means the data are widely scattered.
两个分布可能均值完全相同，但形态截然不同。离散程度的测量描述数据的分散情况。极差是最简单的测量：最高值减最低值。它计算快捷，但只依赖两个案例，一个离群值就能把它毁掉。四分位距——中间 50% 案例所覆盖的范围——则稳健得多。标准差是最有力的测量：它表示每个案例与均值之间的平均距离，因此标准差小意味着数据紧密聚集在均值附近，标准差大则意味着数据广泛分散。
Range = highest value − lowest value | Standard deviation = √(Σ(x − mean)² ÷ n)
6, and the square root gives a standard deviation of approximately 2.4. In a real sociology project this would tell you that the typical case sits about 2.4 units away from the average, information a range alone can never provide.
举例：对于数值 2、4、4、6、9，均值为 25 ÷ 5 = 5。各值与均值之差的平方分别是 9、1、1、1、16，总和为 28。除以 n：28 ÷ 5 = 5.6，开平方得到标准差约为 2.4。在一个真实的社会学项目中，这告诉你"典型"案例距离平均值约 2.4 个单位——这是仅凭极差永远无法提供的信息。
3. Percentages, Proportions and Rates | 百分比、比例与比率
Sociologists rarely report raw numbers, because raw numbers hide the size of the population being studied. Instead they convert data into percentages, proportions and rates. A percentage expresses a part out of one hundred; a proportion is the same idea written as a decimal between 0 and 1; a rate standardises the data to a fixed population unit, usually 1,000 or 100,000 people, so that areas of very different sizes can be compared fairly.
社会学家很少直接报告原始数字，因为原始数字掩盖了被研究人口的规模。他们转而把数据转换为百分比、比例与比率。百分比表示"每一百份中的若干份"；比例是用 0 到 1 之间的小数表达的同一概念；比率则把数据标准化到固定的人口单位，通常为每 1,000 人或每 100,000 人，从而使规模差异极大的地区可以公平比较。
Percentage = (part ÷ whole) × 100 | Proportion = part ÷ whole | Rate per 100,000 = (events ÷ population) × 100,000
offences per 100,000 people. A neighbouring city of 1,000,000 people records 12,000 offences, giving 1,200 per 100,000. The town therefore has the higher rate even though the city recorded more crimes in absolute terms - exactly the kind of comparison that earns evaluation marks.
某镇人口 250,000，一年内记录在案 5,000 起违法案件。犯罪率为 (5,000 ÷ 250,000) × 100,000 = 每十万人 2,000 起。邻近某城市人口 1,000,000，记录 12,000 起，即每十万人 1,200 起。因此尽管城市在绝对数量上犯罪更多，该镇的犯罪率反而更高——这正是能拿到评价分的那类比较。
Percentage change = ((new value − old value) ÷ old value) × 100
ourite exam trap. If the proportion of pupils eligible for free school meals rises from 40% to 50%, the percentage change is ((50 − 40) ÷ 40) × 100 = +25% oints with percentages is one of the most common errors in quantitative sociology answers.
百分比变化是考官最爱的陷阱。如果有资格领取免费校餐的学生比例从 40% 上升到 50%，百分比变化为 ((50 − 40) ÷ 40) × 100 = +25%，但上升幅度是 10 个百分点，而不是 10%。把"百分点"与"百分比"混为一谈，是定量社会学作答中最常见的错误之一。
