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# If x and y are the standard deviations of two different data sets, is

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Math Expert
Joined: 02 Sep 2009
Posts: 51215
If x and y are the standard deviations of two different data sets, is  [#permalink]

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29 Apr 2018, 08:24
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Difficulty:

55% (hard)

Question Stats:

30% (00:49) correct 70% (00:43) wrong based on 80 sessions

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If x and y are the standard deviations of two different data sets, is x > y?

(1) x is the standard deviation of the data set 50, 50, 50, 50, 50, 50, 50, 50 50, 50, 50.
(2) y is the standard deviation of the data set 40, 42, 44, 46, 48, 50, 52, 54 56, 58, 60.

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Joined: 17 May 2015
Posts: 249
Re: If x and y are the standard deviations of two different data sets, is  [#permalink]

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29 Apr 2018, 23:11
3
1
Bunuel wrote:
If x and y are the standard deviations of two different data sets, is x > y?

(1) x is the standard deviation of the data set 50, 50, 50, 50, 50, 50, 50, 50 50, 50, 50.
(2) y is the standard deviation of the data set 40, 42, 44, 46, 48, 50, 52, 54 56, 58, 60.

Hi,

Standard Deviation(SD) is a measure of dispersion of a set of data from its mean. It is the square root of the variance => the minimum value of SD will always be 0.

For more please refer: https://gmatclub.com/forum/math-standar ... 87905.html

Now, let's solve the question.

If x and y are the standard deviations of two different data sets, is x > y?

(1) x is the standard deviation of the data set 50, 50, 50, 50, 50, 50, 50, 50 50, 50, 50.

Since all the data points are same(i.e.50) => x (SD) = 0. Hence, x can't be greater than y. Sufficient.

(2) y is the standard deviation of the data set 40, 42, 44, 46, 48, 50, 52, 54 56, 58, 60.

Definitely value of y is greater than 0, and we have no information about the value of x. Hence, we can't determine whether x is greater than y or not. Insufficient.

Thanks.
Director
Joined: 02 Oct 2017
Posts: 728
Re: If x and y are the standard deviations of two different data sets, is  [#permalink]

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16 May 2018, 06:01
1
) x is the standard deviation of the data set 50, 50, 50, 50, 50, 50, 50, 50 50, 50, 50.

Standard Deviation(SD) is a measure of dispersion of a set of data from its mean. It is the square root of the variance => the minimum value of SD will always be 0.

In this case x=0

Even if y also have same values in its set and y=0

For the same 0>0 not valid

So x>y will be No in every case
So sufficient

(2) y is the standard deviation of the data set 40, 42, 44, 46, 48, 50, 52, 54 56, 58, 60.

Y has got some value here
So can't say. Insufficient

Give kudos if it helps

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Manager
Joined: 19 Aug 2016
Posts: 84
Re: If x and y are the standard deviations of two different data sets, is  [#permalink]

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27 Jun 2018, 19:39
ganand wrote:
Bunuel wrote:
If x and y are the standard deviations of two different data sets, is x > y?

(1) x is the standard deviation of the data set 50, 50, 50, 50, 50, 50, 50, 50 50, 50, 50.
(2) y is the standard deviation of the data set 40, 42, 44, 46, 48, 50, 52, 54 56, 58, 60.

Hi,

Standard Deviation(SD) is a measure of dispersion of a set of data from its mean. It is the square root of the variance => the minimum value of SD will always be 0.

For more please refer: https://gmatclub.com/forum/math-standar ... 87905.html

Now, let's solve the question.

If x and y are the standard deviations of two different data sets, is x > y?

(1) x is the standard deviation of the data set 50, 50, 50, 50, 50, 50, 50, 50 50, 50, 50.

Since all the data points are same(i.e.50) => x (SD) = 0. Hence, x can't be greater than y. Sufficient.

(2) y is the standard deviation of the data set 40, 42, 44, 46, 48, 50, 52, 54 56, 58, 60.

Definitely value of y is greater than 0, and we have no information about the value of x. Hence, we can't determine whether x is greater than y or not. Insufficient.

Thanks.

Hi..

Here we are assuming that the value of Y is greater..without assessing the infor of Y, How can we assume that X >Y?

It can also be the case where the SD of Y could also be 0

Math Expert
Joined: 02 Sep 2009
Posts: 51215
Re: If x and y are the standard deviations of two different data sets, is  [#permalink]

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27 Jun 2018, 20:01
zanaik89 wrote:
ganand wrote:
Bunuel wrote:
If x and y are the standard deviations of two different data sets, is x > y?

(1) x is the standard deviation of the data set 50, 50, 50, 50, 50, 50, 50, 50 50, 50, 50.
(2) y is the standard deviation of the data set 40, 42, 44, 46, 48, 50, 52, 54 56, 58, 60.

Hi,

Standard Deviation(SD) is a measure of dispersion of a set of data from its mean. It is the square root of the variance => the minimum value of SD will always be 0.

For more please refer: https://gmatclub.com/forum/math-standar ... 87905.html

Now, let's solve the question.

If x and y are the standard deviations of two different data sets, is x > y?

(1) x is the standard deviation of the data set 50, 50, 50, 50, 50, 50, 50, 50 50, 50, 50.

Since all the data points are same(i.e.50) => x (SD) = 0. Hence, x can't be greater than y. Sufficient.

(2) y is the standard deviation of the data set 40, 42, 44, 46, 48, 50, 52, 54 56, 58, 60.

Definitely value of y is greater than 0, and we have no information about the value of x. Hence, we can't determine whether x is greater than y or not. Insufficient.

Thanks.

Hi..

Here we are assuming that the value of Y is greater..without assessing the infor of Y, How can we assume that X >Y?

It can also be the case where the SD of Y could also be 0

The standard deviation is always more than or equal to zero: $$SD \ge 0$$. SD is 0 only when the list contains all identical elements (or which is same only 1 element).

(1) implies that x = 0. So, x cannot be more than y because y is 0 or more (so we have a NO answer to the question). If y = 0 too, then x =y, so the answer is still NO.
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Re: If x and y are the standard deviations of two different data sets, is &nbs [#permalink] 27 Jun 2018, 20:01
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