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# Which of the following correctly lists the data sets in order of least

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Math Expert
Joined: 02 Sep 2009
Posts: 61385
Which of the following correctly lists the data sets in order of least  [#permalink]

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23 Dec 2014, 09:06
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Question Stats:

87% (00:42) correct 13% (00:49) wrong based on 124 sessions

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Tough and Tricky questions: Statistics and Sets Problems

Which of the following correctly lists the data sets in order of least to greatest standard deviation?

I. 2, 13, 55, 12, 14, 64
II. 32, 32, 32, 32, 32, 32
III. 37, 38, 39, 40, 41, 42

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

Kudos for a correct solution.

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Joined: 31 Jul 2014
Posts: 125
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Re: Which of the following correctly lists the data sets in order of least  [#permalink]

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24 Dec 2014, 01:58
1
Bunuel wrote:

Tough and Tricky questions: Statistics and Sets Problems

Which of the following correctly lists the data sets in order of least to greatest standard deviation?

I. 2, 13, 55, 12, 14, 64
II. 32, 32, 32, 32, 32, 32
III. 37, 38, 39, 40, 41, 42

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

Kudos for a correct solution.

out of three given sets,
II has all numbers same, so it has zero standard deviation hence it is Least
only answer choices C and D have II in least position.

Out of I ans III
III has consecutive numbers , hence all are closedly spaced hence std deviation will be less
while in I,numbers are spread widely hence std deviation should be more than III

hence order should be II, III,I
IMO D

can someone please validate if this is correct?
Math Expert
Joined: 02 Sep 2009
Posts: 61385
Re: Which of the following correctly lists the data sets in order of least  [#permalink]

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08 Jan 2015, 06:39
Bunuel wrote:

Tough and Tricky questions: Statistics and Sets Problems

Which of the following correctly lists the data sets in order of least to greatest standard deviation?

I. 2, 13, 55, 12, 14, 64
II. 32, 32, 32, 32, 32, 32
III. 37, 38, 39, 40, 41, 42

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

Kudos for a correct solution.

OFFICIAL SOLUTION:

(D) To answer a question such as this, you DO NOT need to know how to calculate standard deviation. You simply need to understand how to compare standard deviations of different sets. The more spread out the numbers are, the greater the standard deviation will be. Even one or two numbers that are much larger or smaller than the others will cause the standard deviation to rise drastically.

Here, there is a very small variation in the terms of set II, so it has the smallest standard deviation. Set III has some variation, but the terms are very close to each other, so it has the next larger standard deviation. Finally, set I has two terms (18 and 64) that are far from the other four terms. Therefore, set I has the largest standard deviation. So the correct order from least to greatest standard deviation is II, III, I.

The correct answer is choice (D).
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Re: Which of the following correctly lists the data sets in order of least  [#permalink]

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08 Jan 2015, 06:51
STANDARD DEVIATION: It is a variation from the mean value or when plotted on graph it shows dispersion from the mean.

So lets see the problem:
I. 2,12,13,14,55,64..................... data are dispersed in wide range from 2 to 64.
II. No deviation as mean is 32 only.
III. Dispersed data but in very low range 37 to 42 as compared to 'I'

Why to take pain of solving it ??

Bunuel wrote:

Tough and Tricky questions: Statistics and Sets Problems

Which of the following correctly lists the data sets in order of least to greatest standard deviation?

I. 2, 13, 55, 12, 14, 64
II. 32, 32, 32, 32, 32, 32
III. 37, 38, 39, 40, 41, 42

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

Kudos for a correct solution.

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Joined: 14 Jul 2014
Posts: 87
Re: Which of the following correctly lists the data sets in order of least  [#permalink]

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26 Jan 2015, 22:22
Bunuel wrote:

Tough and Tricky questions: Statistics and Sets Problems

Which of the following correctly lists the data sets in order of least to greatest standard deviation?

I. 2, 13, 55, 12, 14, 64
II. 32, 32, 32, 32, 32, 32
III. 37, 38, 39, 40, 41, 42

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

Kudos for a correct solution.

Hi Bunuel

I just took the 1st test from 800 score and the official question is as follows

Which of the following correctly lists the data sets in order of least to greatest standard deviation?

I. 18, 25, 25 , 25, 26, 64
II. 32, 32, 32, 30, 32, 32
III. 37, 38, 39, 40, 41, 42

I know I has the greatest SD but I am unable to figure out how to compare II & III - Which has a greater SD ?

Pls explain

Thanks
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Posts: 43
GMAT 1: 600 Q42 V32
GMAT 2: 710 Q48 V38
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Re: Which of the following correctly lists the data sets in order of least  [#permalink]

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29 Dec 2015, 19:11
buddyisraelgmat wrote:
Bunuel wrote:

Tough and Tricky questions: Statistics and Sets Problems

Which of the following correctly lists the data sets in order of least to greatest standard deviation?

I. 2, 13, 55, 12, 14, 64
II. 32, 32, 32, 32, 32, 32
III. 37, 38, 39, 40, 41, 42

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

Kudos for a correct solution.

Hi Bunuel

I just took the 1st test from 800 score and the official question is as follows

Which of the following correctly lists the data sets in order of least to greatest standard deviation?

I. 18, 25, 25 , 25, 26, 64
II. 32, 32, 32, 30, 32, 32
III. 37, 38, 39, 40, 41, 42

I know I has the greatest SD but I am unable to figure out how to compare II & III - Which has a greater SD ?

Pls explain

Thanks

Hi buddyisraelgmat,

Arranging II: 30,32,32,32,32,32. Mean is close to 32- All elements except 30 are 32.
Set III: 37, 38, 39, 40, 41, 42. Mean is 39.5 [ (39+ 40)/2 ]

You can see that the elements in Set III are more widespread from the mean than are the elements in Set II.

Thus SD(III)>SD(II)

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Re: Which of the following correctly lists the data sets in order of least  [#permalink]

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12 Oct 2017, 06:12
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Re: Which of the following correctly lists the data sets in order of least   [#permalink] 12 Oct 2017, 06:12
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