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?

[BTGModeratorVI]

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

Answer: A
Source: Veritas Prep

[Brent@GMATPrepNow]

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

Answer: A
Source: Veritas Prep

-------------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 = 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.
-----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

Cheers,
Brent

[Scott@TargetTestPrep]

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

Answer: A
Source: Veritas Prep

Without the value of x, we see that the mean is (3 + 4)/2 = 3.5. To increase the standard deviation the most, we need a value that is furthermost from 3.5. Therefore, 1 will be the correct answer.

Answer: A

[deloitte247]

Without x, the average/mean of the given set = $$\frac{efx}{ef}=\frac{2+2+3+3+4+4+5+5}{8}=\frac{28}{8}=3.5$$
In order to increase standard deviation, the element/number which has the largest distance from the mean must be added to the existing set.
5 - 3.5 = 1.5
4 - 3.5 = 0.5
3 - 3.5 = 0.5
2 - 3.5 = 1.5
The value of all elements in the set are within $$\pm\ 1.5$$ i.e distance from the mean $$\le1.5$$, for the standard deviation of this set to increase an element/number in which distance from the mean $$>1.5$$ must be added to the set.
1 - 3.5 = - 2.5
Therefore, x = 1 distance between x and mean is > 1.5 so this will increase the standard deviation.
Answer= A