Quote:
If set X and set Y consist of more than one element, what is the ratio of the standard deviation of set X to the standard deviation of set Y?
(1) Set X consists of consecutive multiples of 5 and set Y consists of consecutive multiples of 3
(2) The number of elements in sets X and Y are equal
statement 1: X = {5k, 5k+1, 5k+2, 5k+3...}, Y = {3p, 3p+1, 3p+2, 3p+3...}
we do not know the number of elements in each set, it is required to calculate the standard deviation.
not sufficient.
statement 2: number of elements in X = number of elements in Y.
we do not know the anything about the numbers.
not sufficient
combining both statements,
we know X and Y are evenly space sets with equal number of elements. so the ratio of standard deviation will remain same.
consider X = {5,10,15} Y = {3,6,9}
SD(X) = 5 + 0 + 5 / 3 = 10/3
SD(Y) = 3 + 0 + 3 / 3 = 6/3
ratio = 5/3
consider X = {5,10,15,20,25} Y = {3,6,9,12,15}
SD(X) = 10 + 5 + 0 + 5 + 10 / 5 = 30/5
SD(Y) = 6 + 3 + 0 + 3 + 6 / 5 = 18/5
ratio = 5/3
Ans: C