If set X = {12, 16, 20}, then which of the following sets has a standa

For an even spaced set, SD is directly proportional to the Range.

Only option D has range greater than Set x.

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We see that the given set and all the sets in the answer choices are in an arithmetic progression. We can use the fact that if two sets have the same number of numbers and they are in an arithmetic progression and the set with the larger common difference is the set with a larger standard deviation.

We see that the given set {12, 16, 20} has a common difference of 4. Therefore, we are looking at a set in the answer choices that has a common difference greater than 4. Upon looking at the choices, we see that only {20, 32, 44} has a common difference greater than 4 (its common difference is 12, and all others have a common difference of 4 or less). Therefore, {20, 32, 44} has a larger standard deviation than {12, 16, 20}.

Alternate Solution:

We will use the fact that adding the same number to or subtracting the same number from each element of a set does not change the standard deviation. Let’s add appropriate numbers to each answer choice so that the middle number becomes 16:

A) Add 12 to each element: {14, 16, 18}

B) Add 11 to each element: {15, 16, 17}

C) No need to change the numbers: {13, 16, 19}

D) Subtract 16 from each element: {4, 16, 28}

E) Subtract 83 from each element: {12, 16, 20}

We notice that the mean for each of the sets obtained as above is 16. Since standard deviation is a measure of spread, we should look for the set containing numbers that are furthest away from 16. We notice that the sets in A, B and C have elements that are closer to the mean than set X, while the set in E has the same elements as the set X. The only remaining choice is D.

Answer: D

If set X = {12, 16, 20}, then which of the following sets has a standard deviation greater than that of set X ?

A. {2, 4, 6}
B. {4, 5, 6}
C. {13, 16, 19}
D. {20, 32, 44}
E. {95, 99, 103}

SD of the set is 4, only option D has more than 4.
So, Answer: D

I have bad news and good news.

The bad news is that the standard deviation of {12, 16, 20} is not 4.

The good news that GMAC never asks us to calculate standard deviation.

All we asked to know about standard deviation is that it is a measure of the dispersion of a set.

We can tell that A has a much smaller standard deviation. A is out.
Same for B. B is out.
Not so sure about C, but we notice that the mean is going to be the same as set X and the smaller and larger term are both closer to the mean than set X. C is out.
D. The smallest and largest are each 12 away from the mean. That's a lot more than in set X.
E. Looks like the smallest and largest elements are exactly as far from the mean as in set X, so it's going to have the same standard deviation. E is out.

Answer choice D.

FWIW, I'm not sure GMAC would even have an answer choice like E since we are tasked with knowing that standard deviation has something to do with the mean but aren't tasked with knowing whether it is a function of the mean.