Multiculturalism: A Mathematical Perspective | 多元文化主义的数学视角

📚 Multiculturalism: A Mathematical Perspective | 多元文化主义的数学视角

Multiculturalism is usually explored in sociology or politics, but A-level Mathematics can model cultural diversity using ratios, probability, statistics, and hypothesis testing. This article walks through Edexcel-style techniques applied to multicultural datasets, helping you revise core mathematical methods while seeing how diversity can be quantified and analysed.

多元文化主义通常在社会学或政治学中研究，但 A-level 数学可以通过比、概率、统计和假设检验来对文化多样性进行建模。本文将梳理 Edexcel 风格的解题技巧，并将其应用于多元文化数据集，帮助你复习核心数学方法，同时理解如何量化与分析多样性。

1. Demographic Ratios and Proportion | 人口统计中的比与比例

In a multicultural city, 120 000 residents identify with five main heritage groups A, B, C, D, and E in the ratio 4:3:2:5:1. To find how many residents belong to group D, first add the ratio parts: 4 + 3 + 2 + 5 + 1 = 15. Then multiply the total population by the target part over the total parts.

在一个多元文化城市中，120 000 名居民认同五个主要族群 A、B、C、D、E，比例为 4:3:2:5:1。要求 D 组的人数，先把比例份数相加：4 + 3 + 2 + 5 + 1 = 15。然后用总人口乘以目标份数占总份数的比例。

D = (5 / 15) × 120 000 = 40 000

Always divide the total by the sum of the ratio parts, then multiply by the part you need. This is a basic but frequently examined skill in Edexcel proportion questions.

始终将总数除以比例份数之和，再乘以所需份数。这是 Edexcel 比例题中基础但常考的技能。

2. Index Numbers for Diversity | 多样性的指数

The Simpson diversity index is a common measure of cultural variety. It is defined as D = 1 – Σ p_i², where p_i is the proportion of group i. For two groups with proportions 0.6 and 0.4, the index is calculated as follows.

辛普森多样性指数是衡量文化多样性的常用指标。它定义为 D = 1 – Σ p_i²，其中 p_i 是第 i 组的比例。对于比例为 0.6 和 0.4 的两个群体，该指数计算如下。

D = 1 – (0.6² + 0.4²) = 1 – (0.36 + 0.16) = 0.48

A value closer to 1 indicates higher diversity, while a value closer to 0 suggests one group dominates. This index uses squared proportions, so it connects directly to algebraic substitution and probability notation.

数值越接近 1 表示多样性越高，越接近 0 则表示单一群体占主导。该指数使用比例的平方，因此直接联系代数代入和概率符号。

3. Venn Diagrams and Overlapping Identities | 韦恩图与重叠身份

A survey of 200 adults asks whether they speak English (E) and whether they speak a heritage language (H). 150 speak English, 90 speak the heritage language, and 60 speak both. To find the number who speak exactly one language, subtract the intersection from each total.

一项对 200 名成年人的调查询问他们是否说英语 (E) 以及是否说传承语言 (H)。150 人说英语，90 人说传承语言，60 人两者都说。要求只说一种语言的人数，需要用各总数减去交集。

Only E = 150 – 60 = 90, Only H = 90 – 60 = 30, Exactly one = 90 + 30 = 120

Venn diagrams are useful for overlapping cultural identities because some individuals belong to more than one category. Edexcel often asks you to complete a Venn diagram and interpret regions such as E ∩ H and E’ ∩ H.

韦恩图适用于重叠的文化身份，因为有些人属于多个类别。Edexcel 经常要求你补全韦恩图，并解释 E ∩ H 和 E’ ∩ H 等区域。

4. Probability and Contingency Tables | 概率与列联表

Using the same survey data, a two-way table organises the counts. From the table you can calculate P(E ∪ H) and P(E’ ∩ H) directly by counting favourable outcomes over the total of 200.

使用相同的调查数据，双向表可以整理计数。通过该表，你可以直接用有利结果数除以总数 200 来计算 P(E ∪ H) 和 P(E’ ∩ H)。