Bunuel
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
If you add/subtract the same number from each element of a set, the SD does not change.
I. {r - 2, s - 2, t - 2}
Subtracting 2 from each elements will not change the SD.
II. {0, s - t, s - r}
{s - s, s - t, s - r}
Note that whatever the SD of {s, r, t}, the same will be the SD of {-s, -r, -t} because relative distance between them on the number line does not change (all the numbers are just flipped across the Y axis - positive becomes negative, negative becomes positive).
So, when we add s to each term, we still get the same SD.
III. {|r|, |s|, |t|}
This could change the relative distance between them on the number line if r, s and t all do not have the same sign.
e.g.
______________ (-5)_______________________0______________(3)____(4)
becomes
__________________________________________0______________(3)____(4)____ (5)
Much smaller SD now.
Answer (D)