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The data sets I, II, and III above are ordered from greatest

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The data sets I, II, and III above are ordered from greatest  [#permalink]

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New post 04 Nov 2013, 11:35
1
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A
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I. a-14, a, a, a, a+14
II. b, b+1, b+2, b+3, b+4
III. c, c, c, c, c

The data sets I, II, and III above are ordered from greatest standard deviation to least standard deviation in which of the following?

A. I, II, III
B. I, III, II
C. II, III, I
D. III, I, II
E. III, II, I

I came across the question in GMAT Hacks and well the explanation didn't quite gel or maybe i am missing something.
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Re: Data sets ordering  [#permalink]

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New post 04 Nov 2013, 11:42
sidinsin wrote:
I) a-14, a, a, a, a+14
II) b, b+1, b+2, b+3, b+4
III) c, c, c, c, c

The data sets I, II, and III above are ordered from greatest standard deviation to least standard deviation in which of
the following?
(A) I, II, III
(B) I, III, II
© II, III, I
(D) III, I, II
(E) III, II, I

I came across the question in GMAT Hacks and well the explanation didn't quite gel or maybe i am missing something.


S.D is a non-negative entity. Also, for a given set with all the elements same, the S.D is Zero(It is zero even if there is only one element in the set too). From the given sets, we can see that the last set has a standard deviation of zero. Also, because the other sets can not have all the terms equal for any values of a or b, thus the S.D for the third set(III) has to be the minimum. Select the option which has III in the end.

A.
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Re: Data sets ordering  [#permalink]

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New post 04 Nov 2013, 11:51
mau5, good approach. I was battling between I and II.

The explaination in GMAT hacks insisted that SD for I is less than II and it didn't make any sense.

Thanks
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Re: The data sets I, II, and III above are ordered from greatest  [#permalink]

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New post 05 Nov 2013, 08:37
You can't get a lower SD than with a set of identical numbers (as in III). Therefore A is the only answer.
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Re: The data sets I, II, and III above are ordered from greatest  [#permalink]

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New post 26 Jun 2018, 03:30
In the GMAT, you can think of standard deviation as “the average distance from the mean”

Start with III, it is the simplest:
c, c, c, c, c
mean = c
All of the terms are 0 away from the mean. SD is 0.

Now we have I,and II. The easiest and most intuitive way is to visualize on a horizontal graph where your elements are in the set with your mean of the set in the middle.

So I would look like
a-14___________aaa____________a+14 note that a-14 and a+14 is very far from the mean(mean is a)

and II would look like
b_b+1_b+2_b+3_b+4 note that all the elements are close together (mean = b+2)
and you clearly see I has bigger SD by its definition


Thus A is the answer.
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Re: The data sets I, II, and III above are ordered from greatest &nbs [#permalink] 26 Jun 2018, 03:30
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