A-Level WJEC Sociology: Formula & Theorem Quick Reference Handbook | A-Level WJEC 社会学：公式定理速查手册

📚 A-Level WJEC Sociology: Formula & Theorem Quick Reference Handbook | A-Level WJEC 社会学：公式定理速查手册

Sociology may not have theorems in the mathematical sense, but it relies heavily on statistical formulas and social indicators to analyse social phenomena. This quick reference handbook compiles the essential formulas and definitions that WJEC A-Level Sociology students need for research methods and data interpretation questions. From measures of central tendency to complex indices of inequality, these formulas are the building blocks of quantitative sociological enquiry.

社会学或许没有数学意义上的定理，但它严重依赖统计公式和社会指标来分析社会现象。本速查手册汇集了WJEC A-Level 社会学学生在研究方法和数据解释问题中所需的基本公式和定义。从集中趋势测量到复杂的不平等指数，这些公式是定量社会学探究的基石。

1. Mean, Median and Mode | 平均数、中位数与众数

The mean is the arithmetic average, calculated by summing all values and dividing by the number of cases. It is sensitive to extreme values (outliers).

平均数是算术平均值，通过将所有值相加再除以个案数计算得出。它对极端值（离群值）敏感。

Mean x̄ = Σx / n

where x represents each value and n is the total number of cases.

其中 x 代表每个数值，n 是数据总数。

The median is the middle value when data are ordered from smallest to largest. For an even number of cases, it is the average of the two middle numbers. It is not affected by outliers.

中位数是将数据按从小到大的顺序排列后位于中间的值。当数据个数为偶数时，它是中间两个数的平均值。中位数不受离群值影响。

The mode is the most frequently occurring value in a dataset. It is useful for nominal categories but less reliable for continuous data.

众数是数据集中出现频率最高的值。它对名义分类变量有用，但对于连续数据可靠性较低。

2. Range and Interquartile Range | 全距与四分位距

The range measures dispersion, calculated as the difference between the highest and lowest values. It provides a quick sense of spread but is easily distorted by outliers.

全距衡量离散程度，计算为最大值与最小值之差。它能快速反映数据的分散情况，但容易被离群值扭曲。

Range = Xₘₐₓ – Xₘᵢₙ

The interquartile range (IQR) is the range of the middle 50% of the data, from the lower quartile (Q1) to the upper quartile (Q3). It is robust to outliers.

四分位距（IQR）是中间50%数据的全距，从下四分位数（Q1）到上四分位数（Q3）。它对离群值稳健。

IQR = Q₃ – Q₁

To find Q1 and Q3, the ordered dataset is split after the median value. IQR is often used to construct box plots in sociological reports.

要找到 Q1 和 Q3，需将排序后的数据在中位数之后分开。IQR 常用于在社会学报告中构建箱形图。

3. Variance and Standard Deviation | 方差与标准差

Variance quantifies the average squared deviation of each score from the mean. It provides a measure of data dispersion but is expressed in squared units.

方差量化了每个分数与平均数的离差平方的平均值。它提供了数据分散度的度量，但单位是平方单位。

Variance σ² = Σ(x – x̄)² / n

for a population (use n–1 for a sample). Standard deviation is the square root of variance, returning the measure to original units.

适用于总体（样本则

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