Bunuel wrote:
For the set {2, 2, 3, 3, 4, 4, 5, 5, x}, which of the following values of x will most increase the standard deviation?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
-------------ASIDE----------------
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 =
107 is a distance of 3 from the mean of
109 is a distance of 1 from the mean of
1010 is a distance of 0 from the mean of
1014 is a distance of 4 from the mean of
10So, the average distance from the mean = (3+1+0+4)/4 =
2B {1,8,13,18} Mean =
101 is a distance of 9 from the mean of
108 is a distance of 2 from the mean of
1013 is a distance of 3 from the mean of
1018 is a distance of 8 from the mean of
10So, the average distance from the mean = (9+2+3+8)/4 =
5.5IMPORTANT: 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.
-----ONTO THE QUESTION!!!---------------------------
Remove x from the original set.
The set {2, 2, 3, 3, 4, 4, 5, 5} has a mean of 3.5
In order to affect the greatest increase in the standard deviation, x must be the furthest from the mean (3.5)
Check the answer choices ..... answer choice A is furthest from the mean.
Answer: A
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