Make two data sets have the same standard deviation

Question

I have two different data sets A and B (37 elements each and they have the same mean), and I would like to modify B to have the same standard deviation as A.

I figured to make both have the same mean, I'd have to multiply each element of B by mean(a)/mean(b). But how to make them have the same spread ?

Answer 1

I've figured it out meanwhile, sorry for a quickly closed post ^^

Here is the formula for anyone interested:

$$B = \frac{stDev(A)}{stDev(B)} (B - mean(B)) + mean(B)$$

stdev(S) = Standard Deviation of S