= Relative variance
For a <random variable> $X$ with finite <variance> and nonzero mean, its <relative variance> is $R_X=\operatorname{Var}(X)/(\mathbb EX)^2$. It equals the square of the <coefficient of variation> under the usual positive-mean convention. Multiplying $X$ by a nonzero constant leaves $R_X$ unchanged; adding a constant generally does not.
For an average of $n$ <independent> identically distributed observations with mean $\mu\ne0$ and <variance> $\sigma^2$, the relative <variance> is $\sigma^2/(n\mu^2)$. <Chebyshev's inequality> gives $\mathbb P(|X/\mathbb EX-1|\geq a)\leq R_X/a^2$, explaining its role in <self-averaging>. At zero mean the ratio is undefined, so another reference scale is needed.
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