Standard Deviation Dilema?

Question

(a,b,c,d,e,f) has a mean of X and a Standard Deviation of Y.

What is the mean and standard deviation of (5a, 5b, 5c, 5d, 5e, 5f)

Answer 1

5X and 5Y

There is no work, it is a conceptual question. When you multiply by the same value to each measurement, that mutliplies that value to the mean and multiplies the deviation.

Answer 2

I believe you can pull the 5 out of the set. Then the mean would be 5X.

Variance = standard deviation squared
= Y^2

variance of (5 * set) = (5^2)(variance of set)
= 25(Y^2)
(assuming they are independent)

standard deviation of (5 * set) = sqrt(25(Y^2)) = 5Y.

Answer 3

mean=5*X
var(1st set)=y^2
var(2nd set)
=var(5*1st set)
=5^2*var(1st set) [rules of variance]
=25*Y