V2EX geometric mean

Geometric Mean

释义 Definition

几何平均数:对一组正数取乘积后再开 \(n\) 次方得到的平均值。常用于衡量倍数变化增长率复利等“按比例累积”的情形。公式:
\[ \text{GM}=(x_1x_2\cdots x_n)^{1/n} \] (在统计与数学中很常见;“mean”也可指“平均值/均值”的其他类型。)

发音 Pronunciation (IPA)

/dimtrk min/

例句 Examples

The geometric mean of 4 and 9 is 6.
4 和 9 的几何平均数是 6。

Because investment returns compound multiplicatively, analysts often use the geometric mean to summarize long-term performance across many years.
由于投资回报是以乘法方式复利累积的,分析师常用几何平均数来概括多年期的长期表现。

词源 Etymology

geometric 来自希腊语 geōmetria(“测量土地/几何学”,由 “土地” + metron “测量”构成),引申为“与几何/几何方法相关的”。mean 来自古英语 gemne(“共同的、一般的”),后来在数学语境中发展出“平均值/均值”的含义;合起来即“几何(方式的)平均数”。

相关词 Related Words

文学与著作中的用例 Literary Works

  • Concrete Mathematics(Graham, Knuth, Patashnik):在讨论不等式与平均数时涉及几何平均数。
  • An Introduction to Probability Theory and Its Applications(William Feller):在概率与期望的相关讨论中出现。
  • The Art of Computer Programming(Donald E. Knuth):在算法分析、估计与数值方法相关章节中提及。
  • The Princeton Companion to Mathematics:在数学概念综述与相关条目中出现。
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