Given two populations of ordered/named values, what (if any) is the name of the function given by:
$\sqrt\frac{\sum (x - x^\prime)^2} {\sum x x^\prime}$
where $x$ is the value of a particular measurement in a given sample set and $x^\prime$ the the value of the same measurement in another sample set with which the given set is being compared.
If that doesn't have a name, then is there a name for the inner expression $\frac{\sum (x - x^\prime)^2} {\sum x x^\prime}$, or for either of the sub-expressions $\sum (x - x^\prime)^2$ or $\sum x x^\prime$?
In words, this would the square root of the sum of the square of the differences divided by the sum of the products.
The context is a data scientist has specified this function as the way to measure variance from one sample of (named) data points to the next. I was wondering if there is a name for this particular measurement of variation between one sample and another.
Not central to the problem, but no data is negative, so the product will never be negative, which may have created a problem taking the square root of a negative number if expecting a real result.