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

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

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New post 27 Feb 2019, 23:16
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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}

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Re: If set X = {12, 16, 20}, then which of the following sets has a standa  [#permalink]

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New post 27 Feb 2019, 23:25
D is the answer. SD of the original set is 4 and only the D option offers the SD of 12 which is greater than 4.
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Re: If set X = {12, 16, 20}, then which of the following sets has a standa  [#permalink]

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New post 28 Feb 2019, 03:56
Bunuel wrote:
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 a set is determined along as the variation along mean of set
so for 12,16,20 ; variation along mean is 4 points
and the largest amongst given options is seen in option D as 12 points
IMO D
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Re: If set X = {12, 16, 20}, then which of the following sets has a standa  [#permalink]

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New post 28 Feb 2019, 13:26
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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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Re: If set X = {12, 16, 20}, then which of the following sets has a standa  [#permalink]

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New post 04 Mar 2019, 20:15
Bunuel wrote:
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}


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
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Re: If set X = {12, 16, 20}, then which of the following sets has a standa   [#permalink] 04 Mar 2019, 20:15
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