nikhilgmat31 wrote:Sets A, B, and C are shown below. If the number 100 is added to 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
SD serves to describe how a set of data DEVIATES from the mean.
The MORE a set of data deviates from the mean, the GREATER the SD.
The LESS a set of data deviates from the mean, the LOWER the SD.
A, B and C are all EVENLY SPACED sets.
In an evenly spaced set, mean = median.
Thus, the means for A, B and C are as follows:
A = 70
B = 0
C = 40.
If the number 100 is added to 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?
Since 100 is FURTHEST from B's mean, the SD for B will increase the MOST.
Since 100 is CLOSEST to A's mean, the SD for A will increase the LEAST.
Thus, the order of the increases, from greatest to smallest, is B, C, A.
The correct answer is
E.
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