vjsharma25 wrote:
Sets A, B and C are shown below. If number 100 is included in each of these sets, which of the following represents the correct ordering of the sets in terms of the absolute increase in their standard deviation, from largest to smallest?
A {30, 50, 70, 90, 110}, B {-20, -10, 0, 10, 20}, C {30, 35, 40, 45, 50}
(A) A, C, B
(B) A, B, C
(C) C, A, B
(D) B, A, C
(E) B, C, A
Dear VeritasPrepKarishma,
this is what i found in your post
"If you notice, we have seen two different cases (case 4 and case 5)– in one of them SD increases when you add two numbers to the set and in the other, SD decreases.
Case 4: S = {1, 3, 5} or T = {1, 1, 3, 5, 5} T has higher SD.
It has two extra numbers far from the meanCase 5: S = {1, 3, 5} or T = {1, 3, 3, 5} The standard deviation (SD) of T will be less than the SD of S
So how do you decide whether SD will increase or decrease? Say, what happens in case S = {3, 4, 5, 6, 7} and T = {3, 4, 4, 5, 6, 6, 7}? "
you also said that"If a new element is added which is far away from the mean, it will add much more to the deviations than if it were added close to the mean."
so in case 4: S = {1, 3, 5} ;mean =3 ; the difference of each number of S to mean is 2
T = {1, 1, 3, 5, 5} ; T =3; T added two numbers (1,5) the difference of 1 to the mean(T) of 3 is 2 ; the difference from 5 to the mean(T) of 3 is 2;
my question is why It has two extra numbers far from the mean";