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Is standard deviation of Set A > the standard deviation of Set B? 1)

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Is standard deviation of Set A > the standard deviation of Set B? 1) [#permalink]

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New post 09 Mar 2018, 10:30
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A
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C
D
E

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Is standard deviation of Set A > the standard deviation of Set B?

1) Range of Set A = Range of Set B
2) Number of terms in Set A > Number of terms in Set B

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Is standard deviation of Set A > the standard deviation of Set B? 1) [#permalink]

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New post 09 Mar 2018, 20:03
2
GMATinsight wrote:
Is standard deviation of Set A > the standard deviation of Set B?

1) Range of Set A = Range of Set B
2) Number of terms in Set A > Number of terms in Set B

Source: http://www.GMATinsight.com


We need to know whether elements in Set B are closer than elements in Set A

Statement 1: From this we cannot get a relationship between elements of Set A and Set B

For e.g if Set A=(1,1,1,1,1) & Set B=(2,2), then S.D of A= S.D of B. But if

Set A=(1,2,3,4,5) & Set B=(1,5). Then S.D of A<S.D of B, because within the same range there are more elements in Set A than in Set B. Hence Insufficient

Statement 2: Again if Set A=(1,1,1,1,1) & Set B=(2,2), then S.D of A= S.D of B but if

Set A = (1,10,20,50) & Set B=(1,1), then clearly S.D of A> S.D of B. Hence Insufficient

Combining 1 & 2: We know that the range is same but Set A has more elements than Set B. This implies that within the same boundary limits, there are more numbers in Set A than in Set B.

Hence S.D of A is either less than or Equal to S.D of B but not more than S.D of B. Sufficient

Option C
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Re: Is standard deviation of Set A > the standard deviation of Set B? 1) [#permalink]

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New post 24 Mar 2018, 03:07
Is it C?
If Set A {1,2,6,7} and Set B{1,4,7}
Mean of A = 4. Var = 26,
Mean of B = 4 Var = 18
SD of A = √6.xxx
SD of B = √6
SD of A > SD of B in this instance.
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Re: Is standard deviation of Set A > the standard deviation of Set B? 1) [#permalink]

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New post 24 Mar 2018, 06:07
1
Hi
The answer should be E.

if set A = {1,2,2,3} B ={1,2,3}, SD = SD of A = 0.707, SD of B = 0.816

if set A = {1,1,2,3,3} B ={1,2,3}, SD of A = 0.894, SD of B = 0.816

Hence even after combining Statement A & B, it is not sufficient to answer .

Answer is E

Please clarify and change the OA

GMATinsight wrote:
Is standard deviation of Set A > the standard deviation of Set B?

1) Range of Set A = Range of Set B
2) Number of terms in Set A > Number of terms in Set B

Source: http://www.GMATinsight.com

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Re: Is standard deviation of Set A > the standard deviation of Set B? 1) [#permalink]

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New post 24 Mar 2018, 06:26
I think it should be Answer E.

Standard deviation is the dispersion around the mean. Knowing the relative ranges and/or number of terms does not help us find the mean, nor the dispersion around it.

Let's take 2 examples:
Set A can have 2 data elements, 1 at each extreme, and the rest of the data elements can be right at the mean.
Set B can have all of its data elements at its 2 extremes.
This means (standard deviation of A) < (standard deviation of B)

Or

Set B can have 2 data elements, 1 at each extreme, and the rest of the data elements can be right at the mean.
Set A can have all of its data points at its 2 extremes.
This means (standard deviation of A) > (standard deviation of B)
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Re: Is standard deviation of Set A > the standard deviation of Set B? 1) [#permalink]

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New post 24 Mar 2018, 09:13
gmatbusters wrote:
Hi
The answer should be E.

if set A = {1,2,2,3} B ={1,2,3}, SD = SD of A = 0.707, SD of B = 0.816

if set A = {1,1,2,3,3} B ={1,2,3}, SD of A = 0.894, SD of B = 0.816

Hence even after combining Statement A & B, it is not sufficient to answer .

Answer is E

Please clarify and change the OA

GMATinsight wrote:
Is standard deviation of Set A > the standard deviation of Set B?

1) Range of Set A = Range of Set B
2) Number of terms in Set A > Number of terms in Set B

Source: http://www.GMATinsight.com


Hi gmatbusters

Usually in a set when we say number of terms, it refers to set's cardinal number. so as per statement 2, set's A cardinal number is more than that of set B.

However the illustration that you took, the cardinal number of Set A=Set B (i.e. 1,2,3 in both cases), hence you are getting S.D of A more than S.D of B.

Hi GMATinsight

Kindly clarify Statement 2 of the question because as per your OA it should refer to set's cardinal number (i.e unique elements). In my solution I have assumed that the terms are different and hence got the OA as C
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Re: Is standard deviation of Set A > the standard deviation of Set B? 1) [#permalink]

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New post 24 Mar 2018, 19:30
Dear Sir

1) In statistics question involving mean, standard deviation etc, existence of repeated elements is very common.
We have to take care of repeated elements. Hence I feel we need to take the case of repeated elements also.

2) Secondly if we take all elements different, then also We can have SD of Set A>SD of Set B
eg:
If Set A = {1,1.1,1.2,2,2.8,2.99,3} ; SD = 0.851
If Set B = { 1,2,3} ; SD = 0.816

Hence SD of Set A> SD of Set B

Answer Should be E.


niks18 wrote:
gmatbusters wrote:
Hi
The answer should be E.

if set A = {1,2,2,3} B ={1,2,3}, SD = SD of A = 0.707, SD of B = 0.816

if set A = {1,1,2,3,3} B ={1,2,3}, SD of A = 0.894, SD of B = 0.816

Hence even after combining Statement A & B, it is not sufficient to answer .

Answer is E

Please clarify and change the OA

GMATinsight wrote:
Is standard deviation of Set A > the standard deviation of Set B?

1) Range of Set A = Range of Set B
2) Number of terms in Set A > Number of terms in Set B

Source: http://www.GMATinsight.com


Hi gmatbusters

Usually in a set when we say number of terms, it refers to set's cardinal number. so as per statement 2, set's A cardinal number is more than that of set B.

However the illustration that you took, the cardinal number of Set A=Set B (i.e. 1,2,3 in both cases), hence you are getting S.D of A more than S.D of B.

Hi GMATinsight

Kindly clarify Statement 2 of the question because as per your OA it should refer to set's cardinal number (i.e unique elements). In my solution I have assumed that the terms are different and hence got the OA as C

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Re: Is standard deviation of Set A > the standard deviation of Set B? 1) [#permalink]

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New post 24 Mar 2018, 19:42
1
We can see this like this :
The standard deviation is a widely used concept in statistics and it tells how much variation (spread or dispersion) is in the data set.
Even we have the same range, but since we have number of elements greater in Set A, the new elements in Set A can be
1) Closer to mean : it gives lower SD
2) Closer to the extreme value of set: It gives higher SD.

Hence the SD of Set A can be lower or higher than SD of Set B
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Re: Is standard deviation of Set A > the standard deviation of Set B? 1) [#permalink]

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New post 24 Mar 2018, 21:01
GMATinsight wrote:
Is standard deviation of Set A > the standard deviation of Set B?

1) Range of Set A = Range of Set B
2) Number of terms in Set A > Number of terms in Set B

Source: http://www.GMATinsight.com


Hi GMATinsight

I think the answer should be E.
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Re: Is standard deviation of Set A > the standard deviation of Set B? 1) [#permalink]

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New post 24 Mar 2018, 23:20
Quote:
Dear Sir

1) In statistics question involving mean, standard deviation etc, existence of repeated elements is very common.
We have to take care of repeated elements. Hence I feel we need to take the case of repeated elements also.

2) Secondly if we take all elements different, then also We can have SD of Set A>SD of Set B
eg:
If Set A = {1,1.1,1.2,2,2.8,2.99,3} ; SD = 0.851
If Set B = { 1,2,3} ; SD = 0.816

Hence SD of Set A> SD of Set B

Answer Should be E.


Hi gmatbusters

At first I am no "Sir" buddy, don't make me so old :-D
This is where the confusion is about (and forget about my logic on "number of terms", I guess I was sleeping when I did not realize about non-integer numbers :sad: )

Usually in Statistics we use the formula for Standard Deviation of a "Sample" which is given below -
Attachment:
S.D_Sample.jpg
S.D_Sample.jpg [ 12.56 KiB | Viewed 263 times ]


Whereas GMAT uses the formula for Standard Deviation of a "Population" which ignores "Bessel's Correction" i.e the use of \(n-1\), instead of \(n\)
Attachment:
S.D Population Formula.png
S.D Population Formula.png [ 12.46 KiB | Viewed 263 times ]


So if you are using S.D for population then mathematically you Can get higher S.D for set A than for Set B. But here the author is using S.D for Sample.

unfortunately Mr. Bill Gates (i.e M.S Excel) also uses S.D for sample formula :-D :-D . Generally S.D calculation is not asked in GMAT and while solving this question I used Descriptive statistics tool in excel to calculate S.D, hence I was always getting S.D of A< S.D of B.

Here's your example and you can see how the solution changes -
Attachment:
S.D.jpg
S.D.jpg [ 89.66 KiB | Viewed 263 times ]


Logically speaking as the number of terms in Set A & B are not mentioned, that is they could be a infinite set, so S.D of Sample formula should be used. Also as the boundary of both the sets is fixed and Set A has more elements than Set B so ideally S.D of A<S.D of B

Now it is up to owner of the question GMATinsight to clarify the logic behind the question and solution.

In GMAT although the calculation of S.D is not asked but if required we will have to use formula given in OG i.e. S.D for Population. Hence Your calculation is correct, but the logic behind the question and solution is debatable.
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Is standard deviation of Set A > the standard deviation of Set B? 1) [#permalink]

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New post 25 Mar 2018, 00:33
Hi

Actually, I have taken non integer values arbitrarily. But we can prove the same by integers value also.

Secondly the formula as per GMAT purview is for denominator " n" only.

It was really a nice discussion, it really refreshed my old school concepts.

Thanks to the question.

It seems no one likes my insights, it is quite evident from the absence of any kudos.:)

niks18 wrote:
Quote:
Dear Sir

1) In statistics question involving mean, standard deviation etc, existence of repeated elements is very common.
We have to take care of repeated elements. Hence I feel we need to take the case of repeated elements also.

2) Secondly if we take all elements different, then also We can have SD of Set A>SD of Set B
eg:
If Set A = {1,1.1,1.2,2,2.8,2.99,3} ; SD = 0.851
If Set B = { 1,2,3} ; SD = 0.816

Hence SD of Set A> SD of Set B

Answer Should be E.


Hi gmatbusters

At first I am no "Sir" buddy, don't make me so old :-D
This is where the confusion is about (and forget about my logic on "number of terms", I guess I was sleeping when I did not realize about non-integer numbers :sad: )

Usually in Statistics we use the formula for Standard Deviation of a "Sample" which is given below -
Attachment:
S.D_Sample.jpg


Whereas GMAT uses the formula for Standard Deviation of a "Population" which ignores "Bessel's Correction" i.e the use of \(n-1\), instead of \(n\)
Attachment:
S.D Population Formula.png


So if you are using S.D for population then mathematically you Can get higher S.D for set A than for Set B. But here the author is using S.D for Sample.

unfortunately Mr. Bill Gates (i.e M.S Excel) also uses S.D for sample formula :-D :-D . Generally S.D calculation is not asked in GMAT and while solving this question I used Descriptive statistics tool in excel to calculate S.D, hence I was always getting S.D of A< S.D of B.

Here's your example and you can see how the solution changes -
Attachment:
S.D.jpg


Logically speaking as the number of terms in Set A & B are not mentioned, that is they could be a infinite set, so S.D of Sample formula should be used. Also as the boundary of both the sets is fixed and Set A has more elements than Set B so ideally S.D of A<S.D of B

Now it is up to owner of the question GMATinsight to clarify the logic behind the question and solution.

In GMAT although the calculation of S.D is not asked but if required we will have to use formula given in OG i.e. S.D for Population. Hence Your calculation is correct, but the logic behind the question and solution is debatable.


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Is standard deviation of Set A > the standard deviation of Set B? 1)   [#permalink] 25 Mar 2018, 00:33
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