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MBA Section Director V
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Is the standard deviation of set A is greater than standard  [#permalink]

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Question Stats: 57% (01:03) correct 43% (00:59) wrong based on 223 sessions

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Fantastic Question from VERITAS.
Explain in detail and get a Kudos Reward .

Is the standard deviation of set A is greater than standard deviation of set B ?

1) Set A consists of consecutive multiples of 10

2) Set B consists of consecutive multiples of 2

OA and OE after sufficient discussion.

Happy Solving!!

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Originally posted by Narenn on 16 Oct 2013, 11:27.
Last edited by Narenn on 18 Oct 2013, 12:04, edited 1 time in total.
MBA Section Director V
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Re: Is the standard deviation of set A is greater than standard  [#permalink]

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Thank You Guys for the participation and healthy debate. Here is the OE from Veritas.

A common mistake with standard deviation is focusing only on the spacing of the terms and forgetting about the number of terms.
In this question, each statement alone is clearly insufficient, as you need information about each set to be able to compare standard deviations and answer this question. Hence the answer must be C or E.

In assessing the statements together, be careful about any assumptions you might make. If you have two sets with the same number of terms, then the one that is more spaced (multiples of 10) would indeed have a greater standard deviation than the one that is more narrowly spaced (multiples of 2). However, no information is given here about how many terms are in each set. Since standard deviation is a measure of dispersion around the mean, the number of terms is a hugely important piece of information.

If set B had a million consecutive multiples of 2, it would clearly have a greater standard deviation than set A if it only contained 10 consecutive multiples of 10.

Therefore the relationship between the two standard deviations can not be determined, and the correct answer choice is E

Here are some very good questions on Standard Deviation for Practice. PS DS
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Manager  Joined: 26 Sep 2013
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GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41 Re: Is the standard deviation of set A is greater than standard  [#permalink]

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Narenn wrote:
Fantastic Question from VERITAS.
Explain in detail and get a Kudos Reward .

Is the standard deviation of set A is greater than standard deviation of set B ?

1) Set A consists of consecutive multiples of 10

2) Set B consists of consecutive multiples of 2

OA and OE after sufficient discussion.

Happy Solving!!

I'll go first, but boy do I feel like this is a trap!

I had to choose between C and E....I was thinking E, because you don't know how many numbers are in each set, but then I thought it doesn't matter. So then I thought C because the SD of set A will always be 10, and the SD of set 2 would always be 2. Then I realized that is in fact incorrect; as the numbers get higher, the average gets higher, thus each number is further and further from the average. So I went back to E; because if the set only has one number in it by itself then the SD is 0. If each set has even 2 numbers in it, then A will be higher. Of course, if the wording of the question means that there MUST be more than one number in each set, then the answer would be C.

Thoughts?
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Re: Is the standard deviation of set A is greater than standard  [#permalink]

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Narenn wrote:
Fantastic Question from VERITAS.
Explain in detail and get a Kudos Reward .

Is the standard deviation of set A is greater than standard deviation of set B ?

1) Set A consists of consecutive multiples of 10

2) Set B consists of consecutive multiples of 2

OA and OE after sufficient discussion.

Happy Solving!!

I think the OA is E. If I am correct, below is my explanation.

Key is Set A and Set B not necessarily have the same number of elements

If both set A & set B have the same number of elements, then SD(A) > SD(B)

If set A has just 3 elements and set B has more than 100 + elements, SD (B) > SD (A)

Also, key concept to learn is the set having HIGH RANGE WITH FEW ELEMENTS will have higher SD.
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Re: Is the standard deviation of set A is greater than standard  [#permalink]

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The first thing that comes to my head after reading consecutive multiples it that they are strictly related to each other, which means that adding or subtracting an element from the set will not change the standard deviation.
BUT, when comparing two different sets, it is important to know the number of elements in the set, because the more elements we have the broader they are distributed relative to the mean.
eg std dev of {10,20,30,40} = 12.9 but the std dev of {10,20,30} is just 10. Can see option B the similar way

So the answer is E because knowing the number of elements in the set when comparing standard deviations in a set is important
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Re: Is the standard deviation of set A is greater than standard  [#permalink]

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Narenn wrote:
Fantastic Question from VERITAS.
Explain in detail and get a Kudos Reward .

Is the standard deviation of set A is greater than standard deviation of set B ?

1) Set A consists of consecutive multiples of 10

2) Set B consists of consecutive multiples of 2

OA and OE after sufficient discussion.

Happy Solving!!

Got a Pm..

I really like VERITAS questions....

SD can be simply calculated by knowing the difference between each number on a set.

Statement 1- Is obviously insufficient because it just talks about SET A.

Statement 2- Is again insuff because of the same reason.

Now together they might look sufficient but they are not, simply because there is not information on how many terms are there in each set. If there are equal term then SET A is a winner.

Because of no information the answer is E.
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Re: Is the standard deviation of set A is greater than standard  [#permalink]

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Narenn wrote:
Fantastic Question from VERITAS.
Explain in detail and get a Kudos Reward .

Is the standard deviation of set A is greater than standard deviation of set B ?

1) Set A consists of consecutive multiples of 10

2) Set B consists of consecutive multiples of 2

OA and OE after sufficient discussion.

Happy Solving!!

OA has to be E.

Statement 1 doesn't tell us about the standard deviation of B.
Statement 2 alone doesn't tell us anything about standard deviation of A.

Combining its still insufficient to prove that the SD of A is more than B.If the question would have told us the number of members in each series then both statement together would have been sufficient. Why? See explanation below.

Just pick any number and you will see that the SD of A is always more than B.

Take number 1,2,3,4,5,6....These numbers are neither the consecutive multiple of 2 nor they are consecutive multiples of 10.
However if you multiply them by 2 then you will get 2,4,,6,8,10....
If you multiply the same series by 10 then you will get 10,20,30,40,50,60

So the standard deviation in the consecutive multiples of 10 is always more than consecutive multiples of 2.

Universal rule....Suppose a series of number is A,B,C,D,E,F.....
if you multiple that series by same number then the standard deviation will rise. If you divide the whole series by the same number then SD will reduce.
In the case of multiples of 10 you are basically dividing the whole series by 5 to get consecutive even multiples. Now you might argue that the numbers are not the same in both series. Numbers doesn't matter as we are checking the SD against the mean.
Take example:
10,20,30,40,50,60,70.....consecutive multiples of 10.
2000,2002,2004,2006,2008.....consecutive multiples of 2.

So which one has lower SD. Obviously multiples of 2. So even if the number in consecutive multiples of 2 are bigger we still get SD smaller than consecutive multiples of 10.

To the original question:

You can have multiples of 10 as 10,20...thats it two members.
You can have multiples of 2 as 2,4,6,8,10,12,...2000 in this case SD of the latter is more.

So the final answer is E
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Re: Is the standard deviation of set A is greater than standard  [#permalink]

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The spread of the data set is higher for multiples of 10 than for multiples of 2.
Hence for a given n (# of elements in the set) Std Dev(Set A: Multiples of 10) > Std. Dev (Set B: Multiples of 2).

Now value of n is not provided, but I think for any "n", Std Dev(Set A: Multiples of 10) > Std. Dev (Set B: Multiples of 2).

So (C). Will wait for the OA for the confirmation.
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Re: Is the standard deviation of set A is greater than standard  [#permalink]

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biswasandeep wrote:
The spread of the data set is higher for multiples of 10 than for multiples of 2.
Hence for a given n (# of elements in the set) Std Dev(Set A: Multiples of 10) > Std. Dev (Set B: Multiples of 2).

Now value of n is not provided, but I think for any "n", Std Dev(Set A: Multiples of 10) > Std. Dev (Set B: Multiples of 2).

So (C). Will wait for the OA for the confirmation.

Your reasoning is correct but have a look at my explanation above and you will understand why the OA is E.

Two sets with multiple of 2 and multiple of 10.

10,20….thats it…only 2 numbers in the set.
2,4,,6,8,10,……2000,….2000000….now tell me which set has the more SD. the question didn't tell that the numbers of elements in each set are equal.

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GRE 1: Q169 V154 Re: Is the standard deviation of set A is greater than standard  [#permalink]

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Excellent Question.
Going back to the definition of standard Deviation =>
Standard deviation is a statistical tool used to measure the average distance of individual data elements w.r.t the mean.
Here since no info on the number of elements on both Set A and Set B are given =>We can't comment on their Standard deviation.

Hence E

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Re: Is the standard deviation of set A is greater than standard  [#permalink]

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Statements 1 and 2 each alone are insufficient, since some fact is missing.

Statements 1 and 2 together insufficient, since we have common difference of sequences set A and set B are 10 and 2 but number of terms in each set is unknown.

Standard Deviation of Arithmetic Sequence is d*{sqrt(n^2 - 1 )/12}
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