# How to sum two variables that are on different scales?

If I have two variables following two different distributions and having different standard deviations... How do I need to transform two variables so that when I sum the two result is not "driven" by more volatile one.

For example... Variable A is less volatile than variable B (ranges from 0 to 3000) and variable B goes fro. 300 to 350.

If simply add the two variables together the result will obviously be driven by A.

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A common practice is to standardize the two variables, $A,B$, to place them on the same scale by subtracting the sample mean and dividing by the sample standard deviation. Once you've done this, both variables will be on the same scale in the sense that they each have a sample mean of 0 and sample standard deviation of 1. Thus, they can be added without one variable having an undue influence due simply to scale.
$$\frac{ A - \overline{A} }{ {\rm SD}(A) }, \ \ \frac{ B - \overline{B} }{ {\rm SD}(B) }$$
where $\overline{A}, {\rm SD}(A)$ denotes the sample mean and standard deviation of $A$, and similarly for B. The standardized versions of the variables are interpreted as the number of standard deviations above/below the mean a particular observation is.