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.
--------------------------------
If we apply this definition to the original question, we can see that adding 5 to each of the values has NO EFFECT on their distance from mean. Therefore, the standard deviation will not change.
Cheers,
Brent
Here are a few more practice questions where we can apply the concept of "average distance from the mean" as an approximation for Standard Deviation:
https://www.beatthegmat.com/standard-dev ... 74384.html
https://www.beatthegmat.com/standard-dev ... 69584.html
https://www.beatthegmat.com/range-and-sd-t89159.html
