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

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

ganand · Answer

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.

push12345 · Answer

) 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
Give kudos if it helps

Posted from my mobile device

zanaik89 · Answer

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..

Bunuel · Answer

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.

Izzzaaaaaaaaaa · Answer

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?

Bunuel · Answer

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

quialias · Answer

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.

Bunuel · Answer

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.

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

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

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