Gmat_mission wrote:A set consists of 20 different numbers whose average is 10. Which of the following pairs, when added to the set of numbers, must reduce its standard deviation?
A. 0, 0
B. 0, 20
C. 10, 10
D. -10, 10
E. 5, 15
[spoiler]OA=C[/spoiler]
Source: Veritas Prep
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For the purposes of the GMAT, it's sufficient to think of Standard Deviation as the
Average Distance from the Mean. Here's what I mean:
Consider these two sets: Set A {7,9,10,14} and set B {1,8,13,18}
The mean of set A = 10 and the mean of set B = 10
How do the Standard Deviations compare? Well, since the numbers in set B deviate the more from the mean than do the numbers in set A, we can see that the standard deviation of set B must be greater than the standard deviation of set A.
Alternatively, let's examine the Average Distance from the Mean for each set.
Set A {7,9,10,14}
Mean =
10
7 is a distance of 3 from the mean of
10
9 is a distance of 1 from the mean of
10
10 is a distance of 0 from the mean of
10
14 is a distance of 4 from the mean of
10
So, the average distance from the mean = (3+1+0+4)/4 =
2
B {1,8,13,18}
Mean =
10
1 is a distance of 9 from the mean of
10
8 is a distance of 2 from the mean of
10
13 is a distance of 3 from the mean of
10
18 is a distance of 8 from the mean of
10
So, the average distance from the mean = (9+2+3+8)/4 =
5.5
IMPORTANT: I'm
not saying that the Standard Deviation of set A equals 2, and I'm
not saying that the Standard Deviation of set B equals 5.5 (They are reasonably close however).
What I am saying is that the average distance from the mean can help us see that the standard deviation of set B must be greater than the standard deviation of set A.
More importantly, the average distance from the mean is a useful way to think of standard deviation. This model is a convenient way to handle most standard deviation questions on the GMAT.
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Since all 20 numbers are DIFFERENT, we know that the standard deviation is greater than 0.
Since the mean of the given set is 10, adding two more 10's (both of which are zero units away from the mean) will DECREASE the standard deviation.
Answer: C
Cheers,
Brent
