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SD

by GmatKiss » Tue Nov 01, 2011 5:58 am

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C

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I. 72, 73, 74, 75, 76
II. 74, 74, 74, 74, 74 - S.D = O??!!
III. 62, 74, 74, 74, 89

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
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by shankar.ashwin » Tue Nov 01, 2011 6:07 am
You found Set 2 has 0 SD, so thats comes last. Eliminate A,C,E

Between B and D; Notice numbers in set 1 are closer together and hence would have a smaller SD;

Order should be III,I,II D
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by neelgandham » Tue Nov 01, 2011 6:20 am
I. 72, 73, 74, 75, 76
II. 74, 74, 74, 74, 74
III. 62, 74, 74, 74, 89

calculating the square of the numerator of the Standard deviation formula

(-2)^2 + (-1)^2 + 0^2 + 1^2 + 2^2 = 10
0^2 + 0^2 + 0^2 + 0^2 + 0^2 = 0
(-12)^2 + No need > 144

So III > I > II option D
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by [email protected] » Tue Nov 01, 2011 10:33 pm
Dear Shankar,

what you are saying in right but if we notice in option III middle numbers are same.
So if we say the IIIrd set has higher SD so all the deviations from mean should be same isnt it.

Please correct my understanding
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by shankar.ashwin » Tue Nov 01, 2011 10:55 pm
I am not sure I understand your question properly,

In set III, you have 5 elements of which 3 are equal (74) but the other two elements are quite far off from 74 (12 and 15 units away).
If you notice Set I, its 5 consecutive integers (each differ from the previous by 1)

Imagine plotting the points on a graph, SetI will have all its elements close together whereas SetIII would be scattered, the very definition of SD.
In this case, looking at the numbers we can say its SD would be more than the set with consecutive integers.

But if all the 3 sets had numbers close together, we would need the formula for SD (or) the way 'neelgandham' has posted. That is a foolproof way to do it, but if the numbers given are obvious such as this, I prefer to skip doing math and save time.
[email protected] wrote:Dear Shankar,

what you are saying in right but if we notice in option III middle numbers are same.
So if we say the IIIrd set has higher SD so all the deviations from mean should be same isnt it.

Please correct my understanding
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by [email protected] » Tue Nov 01, 2011 11:18 pm
ok,

i got it now.

"neelgandham " can you please write the formula and its detail which you have used.
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by neelgandham » Wed Nov 02, 2011 2:53 am
[email protected] wrote:ok,

i got it now.

"neelgandham " can you please write the formula and its detail which you have used.
Hello Aksurana,

Please find below the attachment(Self explanatory)
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Re: SD

by Scott@TargetTestPrep » Thu Apr 23, 2020 2:58 am
GmatKiss wrote: ↑
Tue Nov 01, 2011 5:58 am
 I. 72, 73, 74, 75, 76
II. 74, 74, 74, 74, 74 - S.D = O??!!
III. 62, 74, 74, 74, 89

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
Recall that when comparing data sets with the same number of elements, the one with elements spreading out the most has the greatest standard deviation, and the one with elements closest to each other has the least standard deviation. Therefore, set III has the greatest standard deviation (because the elements are spread out the most), set II has the least standard deviation (because all the elements are the same) and set I will have a standard deviation between those of set III and set II.

Answer: D

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