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

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

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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


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[Reveal] Spoiler: OA

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

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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?

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

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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


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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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New post 08 Jan 2015, 07:51
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'

Answer is clearly II, III,I.

Why to take pain of solving it ?? :wink:

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

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New post 26 Jan 2015, 23:22
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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Re: Which of the following correctly lists the data sets in order of least [#permalink]

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New post 29 Dec 2015, 20:11
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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