If d is the standard deviation of x, y, and z, what is the standard deviation of x + 5, y + 5, and z + 5 ?
(A) d
(B) 3d
(C) 15d
(D) d + 5
(E) d + 15
Thanks
(A) d
(B) 3d
(C) 15d
(D) d + 5
(E) d + 15
Thanks
Whenever we change each term in a set by the same value, the standard deviation does not change. We're simply moving the set up or down the number line, so spacing and distance from the mean remain the same. Thus, if the original standard deviation is d, then the standard deviation will still be d after adding 5 to each term.
If our original set was (5, 10, 15), adding 5 creates a new set of (10, 15, 20), which has the same standard deviation.
