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What is the order of the Standard Deviation, from greatest

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What is the order of the Standard Deviation, from greatest [#permalink] New post 15 Oct 2017, 22:54
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What is the order of the Standard Deviation, from greatest to least, of the following three sets?


I. 78, 79, 80, 81, 81
II. 11, 14, 14, 15.5, 17
III. 1.4, 3.9, 7.1, 9.8


(A) I, II, III
(B) II, I, III
(C) III, I, II
(D) III, II, I
(E) None of the above

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[Reveal] Spoiler: OA
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Re: What is the order of the Standard Deviation, from greatest [#permalink] New post 15 Oct 2017, 23:34
Using a bit of intuition, it is clear that the most spread away numbers are those of list III so that it is the one with the highest standard deviation. Thus, we remain with choices C, D, E.

Then, we could easily exclude E, since in order to compute the standard deviation it is enough to have the numbers of the set, thus the comparison is possible.

Now, comparing C and D we can compute the mean and look at the deviation in an approximate way: then, list I has a mean of 79.8, while list II has a mean of 14.3. Thus list II seems more spread around the mean. Or, if we have time, we can compute an approximate sd to confirm our first insight: list I has a approx sd of (1.8+0.8+0.2+1.2+1.2)/5= 1.04, while list II has an approx sd of (3.3+0.3+0.3+1.2+2.7)/5 = 1.56.

To conclude, the order is III, II, I. Answer D
Re: What is the order of the Standard Deviation, from greatest   [#permalink] 15 Oct 2017, 23:34
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What is the order of the Standard Deviation, from greatest

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