<P> where the symbol ∑ ∑ ′ (\ displaystyle \ sideset () (^ (\ prime)) \ sum) indicates that the summation is over only even values of n - 1 - i, i.e., if n is odd, sum over even values of i and if n is even, sum only over odd values of i . </P> <P> This is useful, for instance, in the construction of hypothesis tests or confidence intervals . Statistical inference for the coefficient of variation in normally distributed data is often based on McKay's chi - square approximation for the coefficient of variation </P> <P> According to Liu (2012), Lehmann (1986). "also derived the sample distribution of CV in order to give an exact method for the construction of a confidence interval for CV;" it is based on a non-central t - distribution . </P> <P> Standardized moments are similar ratios, μ k / σ k (\ displaystyle (\ mu _ (k)) / (\ sigma ^ (k))) where μ k (\ displaystyle \ mu _ (k)) is the k moment about the mean, which are also dimensionless and scale invariant . The variance - to - mean ratio, σ 2 / μ (\ displaystyle \ sigma ^ (2) / \ mu), is another similar ratio, but is not dimensionless, and hence not scale invariant . See Normalization (statistics) for further ratios . </P>

A data set has a mean of 129 and a standard deviation of 24. compute the coefficient of variation