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Math Expert V
Joined: 02 Sep 2009
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Is the standard deviation of set A > standard deviation of set B?  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 42% (00:56) correct 58% (00:52) wrong based on 79 sessions

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

(1) Set A consists of consecutive multiples of 10.

(2) Set B consists of consecutive multiples of 2.

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Math Expert V
Joined: 02 Aug 2009
Posts: 8023
Re: Is the standard deviation of set A > standard deviation of set B?  [#permalink]

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PKN wrote:
PKN wrote:
Bunuel wrote:
Is the standard deviation of set A > standard deviation of set B?

(1) Set A consists of consecutive multiples of 10.

(2) Set B consists of consecutive multiples of 2.

Question stem:- Is $$SD_{A}>SD_{B}$$?

Note:- If you multiply the numbers on a list by any values (other than ±1), or if you raise the numbers on a list to a power, that always changes the standard deviation. Multiplying changes the spacing on the list. In particular, if you multiply each number by k, then you multiply the standard deviation by |k|.

St1:- Set A consists of consecutive multiples of 10.
Or A={10,20,30,40,....,10n}
No info on Set B.
Insufficient.

St2:- Set B consists of consecutive multiples of 2
Or, B={2,4,6,8,....,2n}
No info on Set A.
Insufficient.

Combined, Set A can be written as A={5*1,5*2,5*33,5*4,.........} or each term of the set B when multiplied by a constant 5 yield set A.
So, SD of set A=5* SD of set B
Hence $$SD_{A}>SD_{B}$$

Ans. (C)

Hi chetan2u,
Could you please guide me where I am wrong in my explanation above?

Thanking you in advance.

Hi..

You have gone wrong in taking number of elements of each.

Combined..
Set A consists of consecutive multiple of 10, say 10,20
Set B = {2,4,6}
SD of A> SD of B..

But if set A={10,20}
And set B = {2,4,6,8,10,........50}
SD of A<SD of B

Hence E
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Manager  G
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Joined: 11 Jun 2017
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GMAT 1: 630 Q44 V33 GMAT 2: 680 Q47 V37 GPA: 3.2
Is the standard deviation of set A > standard deviation of set B?  [#permalink]

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Bunuel wrote:
Is the standard deviation of set A > standard deviation of set B?

(1) Set A consists of consecutive multiples of 10.

(2) Set B consists of consecutive multiples of 2.

Standard deviation is 0,if all elements are equal.
Also Std deviation is always greater than or equal to zero.
Since by one std deviation we cannot tell for sure if it is less or greater than other deviation,both statements are required.

Ans :C
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Ankit
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Re: Is the standard deviation of set A > standard deviation of set B?  [#permalink]

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Statement 1 doesn't give any info about Set B. Hence insufficient.
Statement 2 doesn't give any info about Set A. Hence insufficient.

Combining both we can say that SD of A will always be greater than B.Irrespective of the number of elements in each set.

C is the answer.

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Re: Is the standard deviation of set A > standard deviation of set B?  [#permalink]

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Bunuel wrote:
Is the standard deviation of set A > standard deviation of set B?

(1) Set A consists of consecutive multiples of 10.

(2) Set B consists of consecutive multiples of 2.

Question stem:- Is $$SD_{A}>SD_{B}$$?

Note:- If you multiply the numbers on a list by any values (other than ±1), or if you raise the numbers on a list to a power, that always changes the standard deviation. Multiplying changes the spacing on the list. In particular, if you multiply each number by k, then you multiply the standard deviation by |k|.

St1:- Set A consists of consecutive multiples of 10.
Or A={10,20,30,40,....,10n}
No info on Set B.
Insufficient.

St2:- Set B consists of consecutive multiples of 2
Or, B={2,4,6,8,....,2n}
No info on Set A.
Insufficient.

Combined, Set A can be written as A={5*1,5*2,5*33,5*4,.........} or each term of the set B when multiplied by a constant 5 yield set A.
So, SD of set A=5* SD of set B
Hence $$SD_{A}>SD_{B}$$

Ans. (C)
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Regards,

PKN

Rise above the storm, you will find the sunshine
VP  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1011
WE: Supply Chain Management (Energy and Utilities)
Re: Is the standard deviation of set A > standard deviation of set B?  [#permalink]

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PKN wrote:
Bunuel wrote:
Is the standard deviation of set A > standard deviation of set B?

(1) Set A consists of consecutive multiples of 10.

(2) Set B consists of consecutive multiples of 2.

Question stem:- Is $$SD_{A}>SD_{B}$$?

Note:- If you multiply the numbers on a list by any values (other than ±1), or if you raise the numbers on a list to a power, that always changes the standard deviation. Multiplying changes the spacing on the list. In particular, if you multiply each number by k, then you multiply the standard deviation by |k|.

St1:- Set A consists of consecutive multiples of 10.
Or A={10,20,30,40,....,10n}
No info on Set B.
Insufficient.

St2:- Set B consists of consecutive multiples of 2
Or, B={2,4,6,8,....,2n}
No info on Set A.
Insufficient.

Combined, Set A can be written as A={5*1,5*2,5*33,5*4,.........} or each term of the set B when multiplied by a constant 5 yield set A.
So, SD of set A=5* SD of set B
Hence $$SD_{A}>SD_{B}$$

Ans. (C)

Hi chetan2u,
Could you please guide me where I am wrong in my explanation above?

Thanking you in advance.
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
Intern  B
Joined: 07 Apr 2019
Posts: 6
Standard deviation of two different sets based on number of elements  [#permalink]

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Hi Experts I came across a statement in a gmat prep material. Tried number picking and checked; I'm not quite convinced.
Seeking experts' opinion: GMATNinja Bunuel VeritasKarishma

The statement goes: "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."

The question : " Is the standard deviation of set A > standard deviation of set B?
(1) Set A consists of consecutive multiples of 10.
(2) Set B consists of consecutive multiples of 2. Standard deviation of two different sets based on number of elements   [#permalink] 18 Sep 2019, 04:26
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