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Bunuel
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If x and y are the standard deviations of two different data sets, is 29 Apr 2018, 09:24
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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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A
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If x and y are the standard deviations of two different data sets, is 30 Apr 2018, 00:11
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Bunuel
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.
Show more

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.

Answer: (A).

Thanks.
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If x and y are the standard deviations of two different data sets, is 16 May 2018, 07:01
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) 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
But no info about x
So can't say. Insufficient

A is answer
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If x and y are the standard deviations of two different data sets, is 27 Jun 2018, 20:39
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ganand
Bunuel
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.

Answer: (A).

Thanks.
Show more

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

Please help..
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If x and y are the standard deviations of two different data sets, is 27 Jun 2018, 21:01
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ganand
Bunuel
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.

Answer: (A).

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

Please help..
Show more

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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If x and y are the standard deviations of two different data sets, is 12 Sep 2025, 02:26
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For statement 1: If x is given to be 50,50....50; why can't we assume y to be something different such as 40,40,---40?
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If x and y are the standard deviations of two different data sets, is Updated on: 12 Sep 2025, 02:44
Originally posted by Bunuel on 12 Sep 2025, 02:43.
Last edited by Bunuel on 12 Sep 2025, 02:44, edited 1 time in total.
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For statement 1: If x is given to be 50,50....50; why can't we assume y to be something different such as 40,40,---40?
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From (1), x = 0. The question asks whether x > y. Since standard deviation cannot be negative, x cannot be greater than y. If the second data set also consists of equal numbers, then y = 0 as well. But even in that case, the answer to the question “whether x > y” will still be No.

BTW, that doubt has already been addressed here: https://gmatclub.com/forum/if-x-and-y-a ... l#p2085351
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If x and y are the standard deviations of two different data sets, is 13 Sep 2025, 22:22
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Ok Considering the answer given by you as A,

Lets say SD of X = 0, which we can easily derive from option A which I agree, but as we dont know the information of SD(Y) we cannot assume that SD of Y will be greater than or equal 0, as we dont have info about SD(Y), as stated by you we cannot directly assume something like that is what I feel.
So correct option is C, is the question was is X>=Y ? then we could have one with A.
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If x and y are the standard deviations of two different data sets, is 14 Sep 2025, 01:55
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quialias

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.

Ok Considering the answer given by you as A,

Lets say SD of X = 0, which we can easily derive from option A which I agree, but as we dont know the information of SD(Y) we cannot assume that SD of Y will be greater than or equal 0, as we dont have info about SD(Y), as stated by you we cannot directly assume something like that is what I feel.
So correct option is C, is the question was is X>=Y ? then we could have one with A.
Show more


You are missing a point. The standard deviation is always greater than or equal to zero. From the first statement, we get that the standard deviation of the set is zero, so x = 0. The question then becomes: is 0 greater than some non-negative number y? Whether y is zero or positive, the answer to “is x > y?” is always no. That’s why statement (1) alone is sufficient. So, A is correct.
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