Ratio of standard deviation to mean Let's say that we have a confidence interval like this: µ ± σ, where σ is the standard deviation and µ is the mean. I want to know if the ratio σ/µ has any interpretation? Does it mean anything if we evaluate it?
Thank you in advance!
 A: Yes, it does have an interpretation. That ratio is called the Coefficient of Variation(CV) and it shows the magnitude of variation in relation to the population mean. It is used to describe the variation within the data without depending on the measurement unit of the data, so you can easily compare the dispersion across different distributions of data Please check out CV wikipedia or This Link for more information.
NOTE: This statistic is only meaningful for ratio variables, which are variables that have a clear definition of 0(e.g. 0 means none of that variable).
A: The inverse of this generalizes to n dimensions https://en.wikipedia.org/wiki/Mahalanobis_distance , and basically is a distance scaled by the covariance matrix.  It tells you how many "sigmas" out a point is ellipsoidally along its covariance. In this case, "sigma" means sqrt(eigenvalue).  Square root of eigenvalues are the standard deviations in the "independent" coordinate frame, i.e., when the covariance is rotated so that its eigenvectors align with the coordinate axes.
