Remember the following two things about standard deviation...
#1. When all the elements of a set is increased or decreased by the same amount, the standard deviation does not change.
#2. When all the elements of a set is multiplied by a constant k, the new standard deviation is |k|*(old standard deviation)

Now, option I can be obtained by decreasing all the elements of the given set by 2.
So, standard deviation of {r - 2, s - 2, t -2} = standard deviation of {s, r, t}

Option II can be obtained by multiplying {s, r, t} by -1 and then adding s to all the elements.
So, standard deviation of {0, s - t, s - r} = |-1|*(standard deviation of {s, r, t}) = standard deviation of {s, r, t}

So, I and II will have same standard deviation as {s, r, t}
Only option D contains both of these.

Answer : D

vipulgoyal wrote:Which of the following has the same standard deviation as {s,r,t}?
I. {r-2, s-2, t-2}
II. {0, s-t, s-r}
III. {|r|, |s|, |t|}
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only

Standard deviation describes the SPREAD of the data.

Since statement III includes absolute value, plug in a random combination of positive and negative values.
Let s=-2, r=-1, and t=2.
Here, there is a distance of 1 (between s and r) and a distance of 3 (between -1 and 2).
Any statement that yields a distance of 1 and a distance of 3 will have the same standard deviation.

I: r-2, s-2, t-2
-1-2, -2-2, 2-2
-3, -4, 0
-4, -3, 0.
Here, there is a distance of 1 (between -4 and -3) and a distance of 3 (between -3 and 0).
Eliminate B and C, which do not include statement I.

II: {0, s-t, s-r}
0, -2-2, -2-(-1)
0, -4, -1
-4, -1, 0.
Here, there is a distance of 1 (between -1 and 0) and a distance of 3 (between -4 and -1).
Eliminate A and E, which do not include statement II.

The correct answer is D.

Statement III: {|r|, |s|, |t|}
|-1|, |-2|, |2|
1, 2, 2.
Here, there is a distance of 0 (between 2 and 2) and a distance of 1 (between 1 and 2).
Since statement III does not yield a distance of 1 and a distance of 3, it will not have the same standard deviation as {s, r, t}.