Standard Deviation Dilema?

(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)

Standard Deviation Dilema?
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.
Reply: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
Reply: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.