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Are the standard deviations of set A and set B the same? 1) n=6 2) S

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Are the standard deviations of set A and set B the same? 1) n=6 2) S  [#permalink]

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New post 21 Feb 2017, 17:46
1
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Are the standard deviations of set A and set B the same?

1) n = 6
2) Set A = {n, 2, 2, 2} and set B = {n, n, n, 2}

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Are the standard deviations of set A and set B the same? 1) n=6 2) S  [#permalink]

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New post 23 Feb 2017, 12:33
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AustinKL wrote:
Are the standard deviations of set A and set B the same?

1) n = 6
2) Set A = {n, 2, 2, 2} and set B = {n, n, n, 2}

Dear AustinKL,

I'm happy to respond. :-) This is a great question! You may find this blog article germane:
Standard Deviation on the GMAT

Statement #1: n = 6
Obviously, this statement, alone and by itself, is not sufficient.

Statement #1: Set A = {n, 2, 2, 2} and set B = {n, n, n, 2}
This statement is the meat of the question!

Standard deviation is a way to measure the spread of a set. It only depends on the spacing of the numbers. Here's what I mean. Consider
Set #1 = {1, 4, 9, 16, 25}
That's the first five squares. The "spacings" in that set could be written as _3_5_7_9_. Any other set with that same pattern of spacing, or the mirror image, would have the same SD. Such other sets would include:
Set #2 = {21, 24, 29, 36, 45}
Set #3 = {-11, -8, -3, 4, 13}
Set #4 = {22, 31, 38, 43, 46}
That last set has the "spacings" in the reverse order. That doesn't matter. As long as the set of spacings is the same, the SD is the same. All four of these sets have the same SD. If you think of each set as a set of five dots on the number line, notice that each set is the same pattern of dots--we could just slide the pattern up or down the number line, or flip it around & slide it in the case of set 4.
Attachment:
sets on number line.png
sets on number line.png [ 43.77 KiB | Viewed 945 times ]


Now, consider the two sets given in this statement: Set A = {n, 2, 2, 2} and set B = {n, n, n, 2}. Let say the distance between n and 2 is D = |n - 2|. In both sets, we have three dots in one place and one dot that is D units away from those three. Thus, we have the same "spacings," the same pattern of dots, in both sets. Both sets have the same S.D. We can give a definitive "yes" to the prompt question. Because we have enough information to give a definitive answer, this statement, alone and by itself, is sufficient.

OA = (B)

Does all this make sense?
Mike :-)
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Re: Are the standard deviations of set A and set B the same? 1) n=6 2) S  [#permalink]

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New post 03 Mar 2017, 03:18
the answer should be B
although C is tempting but if we put any value in place of n then the s.d. will always be the same.
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Re: Are the standard deviations of set A and set B the same? 1) n=6 2) S  [#permalink]

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New post 14 Mar 2017, 08:20
Very nice one.
It shows that SD measure the actually the "Dispersion" around the average value of the items.

(1)- Not sufficient
(2)- Sufficient. Can be done by trying different value of n.
Below is a formula approach
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Re: Are the standard deviations of set A and set B the same? 1) n=6 2) S  [#permalink]

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New post 26 Mar 2019, 06:35
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Re: Are the standard deviations of set A and set B the same? 1) n=6 2) S   [#permalink] 26 Mar 2019, 06:35
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