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07 Apr 2018, 13:47
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
39% (01:18) correct
61%
(01:10)
wrong
based on 822
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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
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
08 Apr 2018, 08:11
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I think the answer is D.
I. {r - 2, s - 2, t - 2}
If every element in a set is increased/decreased by a constant, c, the standard deviation does not change. Thus, this set has the same standard deviation as {s, r, t}.
II. {0, s - t, s - r}
We can subtract constant, s, from each of the 3 elements in this set and not change the standard deviation.
The set becomes: {-s, -t, -r}
This is a mirror image of {s,t,r}. The relative positions of {-s,-t,-r} on the number line are the same as the relative positions of {s, r, t}. Thus, standard deviation is the same.
III. {|r|, |s|, |t|}
If {r,s,t} = {-1,1,1}, we have some positive standard deviation.
Then {|r|, |s|, |t|} = {1,1,1}, which has standard deviation = 0.
I. {r - 2, s - 2, t - 2}
If every element in a set is increased/decreased by a constant, c, the standard deviation does not change. Thus, this set has the same standard deviation as {s, r, t}.
II. {0, s - t, s - r}
We can subtract constant, s, from each of the 3 elements in this set and not change the standard deviation.
The set becomes: {-s, -t, -r}
This is a mirror image of {s,t,r}. The relative positions of {-s,-t,-r} on the number line are the same as the relative positions of {s, r, t}. Thus, standard deviation is the same.
III. {|r|, |s|, |t|}
If {r,s,t} = {-1,1,1}, we have some positive standard deviation.
Then {|r|, |s|, |t|} = {1,1,1}, which has standard deviation = 0.
Bunuel
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)
