Author 
Message 
TAGS:

Hide Tags

SVP
Joined: 08 Jul 2010
Posts: 2114
Location: India
GMAT: INSIGHT
WE: Education (Education)

Is standard deviation of Set A > the standard deviation of Set B? 1) [#permalink]
Show Tags
09 Mar 2018, 10:30
Question Stats:
20% (01:04) correct 80% (00:42) wrong based on 69 sessions
HideShow timer Statistics
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: www.GMATinsight.com
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1141
Location: India
GPA: 3.82

Is standard deviation of Set A > the standard deviation of Set B? 1) [#permalink]
Show Tags
09 Mar 2018, 20:03
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.comWe 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 InsufficientStatement 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 InsufficientCombining 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. SufficientOption C



Intern
Joined: 01 Feb 2018
Posts: 3

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



DS Forum Moderator
Joined: 27 Oct 2017
Posts: 561
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)

Re: Is standard deviation of Set A > the standard deviation of Set B? 1) [#permalink]
Show Tags
24 Mar 2018, 06:07
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 EPlease 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
_________________
SC: Confusable words All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory Error log/Key Concepts Combination Concept: Division into groups Question of the Day (QOTD) Free GMAT CATS



Manager
Joined: 30 Mar 2017
Posts: 113

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



PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1141
Location: India
GPA: 3.82

Re: Is standard deviation of Set A > the standard deviation of Set B? 1) [#permalink]
Show Tags
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 EPlease 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.comHi gmatbustersUsually 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 GMATinsightKindly 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



DS Forum Moderator
Joined: 27 Oct 2017
Posts: 561
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)

Re: Is standard deviation of Set A > the standard deviation of Set B? 1) [#permalink]
Show Tags
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 Beg: 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 EPlease 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.comHi gmatbustersUsually 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 GMATinsightKindly 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
_________________
SC: Confusable words All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory Error log/Key Concepts Combination Concept: Division into groups Question of the Day (QOTD) Free GMAT CATS



DS Forum Moderator
Joined: 27 Oct 2017
Posts: 561
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)

Re: Is standard deviation of Set A > the standard deviation of Set B? 1) [#permalink]
Show Tags
24 Mar 2018, 19:42
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
_________________
SC: Confusable words All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory Error log/Key Concepts Combination Concept: Division into groups Question of the Day (QOTD) Free GMAT CATS



Senior Manager
Joined: 31 Jul 2017
Posts: 368
Location: Malaysia
WE: Consulting (Energy and Utilities)

Re: Is standard deviation of Set A > the standard deviation of Set B? 1) [#permalink]
Show Tags
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.comHi GMATinsightI think the answer should be E.
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!



PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1141
Location: India
GPA: 3.82

Re: Is standard deviation of Set A > the standard deviation of Set B? 1) [#permalink]
Show Tags
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 gmatbustersAt first I am no "Sir" buddy, don't make me so old 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 noninteger numbers ) Usually in Statistics we use the formula for Standard Deviation of a "Sample" which is given below  Attachment:
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 \(n1\), instead of \(n\) Attachment:
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 . 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 [ 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.



DS Forum Moderator
Joined: 27 Oct 2017
Posts: 561
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)

Is standard deviation of Set A > the standard deviation of Set B? 1) [#permalink]
Show Tags
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 gmatbustersAt first I am no "Sir" buddy, don't make me so old 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 noninteger numbers ) 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 \(n1\), 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 . 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. Posted from my mobile device
_________________
SC: Confusable words All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory Error log/Key Concepts Combination Concept: Division into groups Question of the Day (QOTD) Free GMAT CATS




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






