If sets X and Y have an equal number of elements, does set X have a

Question

If sets X and Y have an equal number of elements, does set X have a greater standard deviation than set Y?

(1) The difference between each pair of the neighboring elements is consistent throughout each set;
(2) Each of the first two elements in Set Y is twice greater than the corresponding first and second elements in Set X.

iamgame · Accepted Answer

Standard Deviation by definition shows how much variation or "dispersion" there is from the average (mean, or expected value).
https://en.wikipedia.org/wiki/Standard_deviation
Speaking in simplified language a higher SD will mean large range of members (members with individual values farther from the mean) and a low SD will mean closely clustered members (members with individual values very close to the mean).
Now coming to the question:
does set X have a greater standard deviation than set Y?
Statements:
(1) The difference between each pair of the neighboring elements is consistent throughout each set
Does not give relation between set X and Set Y - Insufficient. Though it means that the members are evenly placed in either of the sets, we cannot determine whether they are closely packed or widely distributed.
Eg. X can be {1,3,5,7,9} SD ~ 2.82
Y can be {2,5,8,11,14} SD ~ 4.24

(2) Each of the first two elements in Set Y is twice greater than the corresponding first and second elements
Gives relation only between the first 2 elements between the 2 sets, we cannot determine the other elements or their distribution. -> Insufficient.

A and B together can give us insight into the whole set for both X and Y.
if X is {1,3,5,7,9}
Y has to be 2,6,10,14,18

Hence we can determine if the SD of X is greater than SD of Y which in this case would be 5.65

Hence C

IanStewart · Answer

Where are these questions from? You've tagged this as a GMATPrep question, but it certainly is not from GMATPrep, since it doesn't make any mathematical sense. The elements in a set are not in any order, so the wording in each of the Statements is nonsensical - a set doesn't have a 'first element', a 'second element', or 'neighboring elements'.

In any case, I think Statement 2 means to say that the two smallest elements in Set Y are twice greater than the two smallest elements in Set X. Then Statement 1 is not sufficient alone - it only tells us the two sets are equally spaced. Whichever set has the greatest distances separating elements will have the greater standard deviation, but we don't know in which set the spacing is larger. Statement 2 alone only discusses two elements in each set, and standard deviation is based on every element in a set, so Statement 2 cannot possibly be sufficient.

Taking the two Statements together, they are almost sufficient, at least if we assume Statement 2 is talking about the two smallest elements in each set. If we assume that the elements in each set are all distinct, then if x and y are the two smallest elements in the first set, then 2x and 2y are the two smallest elements in the second set. Thus the spacing in the second set is 2y - 2x = 2(y -x), so is twice as large as the spacing in the first set. Since the sets have the same number of elements but those elements are further apart in the second set, the second set will have a larger standard deviation.

There is, however, one technicality that prevents the two statements together from being sufficient: it is possible that the standard deviation of each set is 0. That is, it's possible, even using both statements, that all of the elements in each set are identical. I would guess whoever designed the question meant to make clear that the elements were different in each set, because it's not a very interesting question if the elements can all be the same, but it's a very badly worded question to begin with. I don't know what "Ivy 6" means - what is that?

iamgame · Answer

That said, i agree with IanStewart completely. I had to make a lot of assumptions to arrive at this answer. Should not be the case with the actual test. This question is very ambigous and can be answered in many ways with different Options.

enigma123 · Answer

I agree with you all. Ivy is the name of the book that I am following and some questions are really vague. My apologies.

alphabeta1234 · Answer

If sets X and Y have an equal number of elements, does set X have a greater standard deviation than set Y?

(1) The difference between each pair of the neighboring elements is consistent throughout each set;
(2) Each of the first two elements in Set Y is twice greater than the corresponding first and second elements in Set X.

Solution

Solution:

1) We are told that both sets are arithmetic progressions. Although both sets X and Y have the same number of elements, a very important fact, the statement neither specifies the distributions of the arithmetic sequence for each of the sets NOR a relationship between how the arthimetic progression between the two sets relate. Either would have done. Ex.

X={2,4,6,8,10} A.P. with spacing of 2
Y={5,10,15,20,25} A.P with spacing of 5.

In this case Y has a higher standard deviation(large spacing) than X. The reverse could be flipped:

X={6,12,18,24,30} A.P. with spacing of 6
Y={5,10,15,20,25} A.P with spacing of 5.

In this case X has a higher standard deviation(large spacing) than Y.

2) Doesn't tell us how the numbers after the first two terms play out. Ex:

X={3,7,10000}
Y={6,14,20}

X has the larger SD in this example.

X={3,7,5}
Y={6,14,2000}

Y has the larger SD in this example.

Hence INSUFF

(1) & (2)

AP for both sets and Y doubles the first two elements of X.

X={a,a+2,a+4,.....} spacing of 2
Y={2a,2a+4,2a+6....} spacing of 4 imposed on all the numbers since we have an A.P.

Notice we now have a relationship between the two sets. The spacing for Y is double that of X. Hence SUFF.

Bunuel · Answer

The wording of this question is quite ambiguous and non-GMAT like:

1. Sets are not ordered by definition. So, "the first two elements in Set" doesn't make any sense.
2. "Twice greater" and "consistent throughout each set" is not the wording you'll see on the GMAT.

So, I wouldn't worry about this question at all.

alphabeta1234 · Answer

Your absolutly right! That slipped my mind. Nonetheless the writer of the questions intent was that the set is sequntielly ordered. If that were the case the answer would be (C)

If sets X and Y have an equal number of elements, does set X have a

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