Editing Geometric mean (section)

===Comparison to arithmetic mean===
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{{main|Inequality of arithmetic and geometric means}}
The geometric mean of a non-empty data set of positive numbers is always at most their arithmetic mean. Equality is only obtained when all numbers in the data set are equal; otherwise, the geometric mean is smaller. For example, the geometric mean of 2 and 3 is 2.45, while their arithmetic mean is 2.5. In particular, this means that when a set of non-identical numbers is subjected to a [[mean-preserving spread]] — that is, the elements of the set are "spread apart" more from each other while leaving the arithmetic mean unchanged — their geometric mean decreases.<ref>{{cite journal |last=Mitchell |first=Douglas W. |title=More on spreads and non-arithmetic means |journal=[[The Mathematical Gazette]] |volume=88 |year=2004 |issue=511 |pages=142–144 |doi=10.1017/S0025557200174534 |s2cid=168239991 }}</ref>