A-Level Edexcel Maths: Data, Probability and Projectiles in the Franco-Prussian War 1862–71 | 爱德思A-Level数学：普法战争1862–71中的数据、概率与抛体运动

📚 A-Level Edexcel Maths: Data, Probability and Projectiles in the Franco-Prussian War 1862–71 | 爱德思A-Level数学：普法战争1862–71中的数据、概率与抛体运动

Although the period 1862–71 is often studied as the road to German unification, this Edexcel A-Level Maths article uses the Franco-Prussian context to practise statistics, probability and mechanics. Military records, casualty figures, artillery ranges and supply logistics provide realistic data for the mathematical techniques required by the Edexcel specification.

尽管1862–71年常作为德意志统一的历史背景被学习，但本文以普法战争为情境，练习Edexcel A-Level数学中的统计、概率和力学。军事记录、伤亡数字、火炮射程与补给后勤为Edexcel考纲要求的数学方法提供了真实数据。

1. Types of Data from Military Records | 军事记录中的数据类型

Quantitative data can be discrete or continuous. For example, the number of artillery pieces in a Prussian corps is discrete because it takes whole-number values. The range of a French mitrailleuse is continuous because it can take any value in an interval.

定量数据可以是离散型或连续型。例如，普鲁士一个军的火炮数量是离散数据，因为它取整数值；法国机枪的射程是连续数据，因为它可以在一个区间内取任意值。

The Edexcel exam often asks you to classify variables as qualitative, quantitative discrete or quantitative continuous. Always link your answer to the context rather than just writing ‘number’.

Edexcel考试常要求你将变量分类为定性、定量离散或定量连续。回答时一定要结合情境，而不要只写“数量”。

2. Measures of Central Tendency | 集中趋势的度量

For ungrouped data, the mean is given by x̄ = Σx / n. If a sample of 8 French cavalry regiments had remount needs of 12, 15, 18, 22, 25, 28, 31 and 37 horses, the mean is (12 + 15 + 18 + 22 + 25 + 28 + 31 + 37) / 8 = 23.5 horses.

对于未分组数据，均值公式为 x̄ = Σx / n。如果8个法国骑兵团的补马需求为12、15、18、22、25、28、31和37匹，则均值为(12+15+18+22+25+28+31+37)/8 = 23.5匹。

The median is the middle value when the data are ordered. Here the ordered data have median (22 + 25) / 2 = 23.5, which

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