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# Is the standard deviation of Set A greater than or equal to the standa

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Math Expert
Joined: 02 Sep 2009
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Is the standard deviation of Set A greater than or equal to the standa  [#permalink]

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11 Apr 2018, 20:23
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5% (low)

Question Stats:

85% (00:52) correct 15% (01:29) wrong based on 61 sessions

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Is the standard deviation of Set A greater than or equal to the standard deviation of Set B?

(1) Set B can be formed by dividing each value in Set A by 4.

(2) Set A consists of 7 unique numbers.

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Is the standard deviation of Set A greater than or equal to the standa  [#permalink]

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12 Apr 2018, 05:06
Bunuel wrote:
Is the standard deviation of Set A greater than or equal to the standard deviation of Set B?

(1) Set B can be formed by dividing each value in Set A by 4.

(2) Set A consists of 7 unique numbers.

Question : Is Standard Deviation of A > Standard deviation of B?

Statement 1: Set B can be formed by dividing each value in Set A by 4.

Since each value of A is divided by 4 to obtain each value of Set B therefore the gaps among the values will also be divided by 4 hence standard deviation will decrease hence

Standard Deviation of A > Standard deviation of B

SUFFICIENT

Statement 2: Set A consists of 7 unique numbers

No Information of Set B hence

NOT SUFFICIENT

CONCEPT TABLE ON STANDARD DEVIATION

STANDARD DEVIATION
Standard Deviation : Average Deviation of Terms of a set from the Mean value of the Set
1) If we had assumed that all barrels had the same amount of mixture then standard deviation would have been zero. Non Zero standard deviation means that all barrels don't have the same amount of Mixture and the the size of Barrels doesn't matter, all that matters is the amount of Mixture in the barrels

2) The standard deviation of a set doesn't change if a constant is added to/subtracted from each terms of the set
e.g.{1, 2, 3, 4, 5} will have same standard Deviation as {1+10, 2+10, 3+10, 4+10, 5+10}
Reason: The deviation remains same as before if the constant is added to/Subtracted from each term

3) Standard Deviation of the Set changes when a constant term which is not equal to 1 is multiplied with/divides every terms of the set
e.g. {0.7, 1.4, 2.1, 2.8, 3.5} will have Standard Deviation = 0.7* Standard deviation of set {1, 2, 3, 4, 5}
Reason: The deviation gets multiplied by or divided by the same constant that every terms is multiplied or divided with
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Re: Is the standard deviation of Set A greater than or equal to the standa  [#permalink]

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12 Apr 2018, 06:51
IMO A

St1 implies that sd in b will decrease compared to A as every term is divided by 4
St2 can't say anything about sd
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Re: Is the standard deviation of Set A greater than or equal to the standa  [#permalink]

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13 Apr 2018, 11:45
uhm no - the answer is C.

Even if all the values in B are 4 times the value in A, if they are all the same - meaning not unique then both sets have SDs of 0.
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Is the standard deviation of Set A greater than or equal to the standa  [#permalink]

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Updated on: 30 Apr 2018, 07:29
I)There is no impact on standard deviation if constant term is added , subtracted
Sd remains same
So sd of A=sd of B
Sufficient

II)no info abt set B
Insufficient

So ans A

Posted from my mobile device
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Originally posted by push12345 on 23 Apr 2018, 09:20.
Last edited by push12345 on 30 Apr 2018, 07:29, edited 1 time in total.
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Is the standard deviation of Set A greater than or equal to the standa  [#permalink]

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30 Apr 2018, 05:22
push12345 wrote:
I)There is no impact on standard deviation if constant term is added , subtracted ,multiplied or divided.
Sd remains same
So sd of A=sd of B
Sufficient

II)no info abt set B
Insufficient

So ans A

Posted from my mobile device

I am confused between your explanation and GMATinsight as to whether the Standard deviation will increase or remain same.

But I think if all the values are multiplied by 4, then the distances among them will be high and hence, SD will be higher in set A.

Can you please confirm this Bunuel.
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Re: Is the standard deviation of Set A greater than or equal to the standa  [#permalink]

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30 Apr 2018, 07:30
hero_with_1000_faces

Yes you are correct.subtraction and addition doesn't change SD
But multiply or divide does.

I have edited my explanation above

Posted from my mobile device
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Re: Is the standard deviation of Set A greater than or equal to the standa  [#permalink]

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01 May 2018, 00:30
hero_with_1000_faces wrote:
push12345 wrote:
I)There is no impact on standard deviation if constant term is added , subtracted ,multiplied or divided.
Sd remains same
So sd of A=sd of B
Sufficient

II)no info abt set B
Insufficient

So ans A

Posted from my mobile device

I am confused between your explanation and GMATinsight as to whether the Standard deviation will increase or remain same.

But I think if all the values are multiplied by 4, then the distances among them will be high and hence, SD will be higher in set A.

Can you please confirm this Bunuel.

hero_with_1000_faces

What I stated is perfectly fine.

When you tend to get confused between statement of two individuals then see who has the expert tag... trust that statement more which comes from an expert..

Not to mention that even experts make mistakes occasionally so we can always debate any doubt further.
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Re: Is the standard deviation of Set A greater than or equal to the standa &nbs [#permalink] 01 May 2018, 00:30
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