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Intern  Joined: 08 Mar 2011
Posts: 15
Set A consists of all even integers between 2 and 100  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 66% (01:52) correct 34% (02:03) wrong based on 470 sessions

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Set A consists of all even integers between 2 and 100, inclusive. Set X is derived by reducing each term in set A by 50, set Y is derived by multiplying each term in set A by 1.5, and set Z is derived by dividing each term in set A by -4. Which of the following represents the ranking of the three sets in descending order of standard deviation?

(A) X, Y, Z
(B) X, Z, Y
(C) Y, Z, X
(D) Y, X, Z
(E) Z, Y, X

Originally posted by punyadeep on 14 Mar 2011, 09:20.
Last edited by Bunuel on 17 Jul 2012, 03:34, edited 1 time in total.
Edited the OA.
Math Expert V
Joined: 02 Sep 2009
Posts: 58435
Re: std deviation  [#permalink]

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5
6
Set A consists of all even integers between 2 and 100, inclusive. Set X is derived by reducing each term in set A by 50, set Y is derived by multiplying each term in set A by 1.5, and set Z is derived by dividing each term in set A by -4. Which of the following represents the ranking of the three sets in descending order of standard deviation?
(A) X, Y, Z
(B) X, Z, Y
(C) Y, Z, X
(D) Y, X, Z
(E) Z, Y, X

pls explain the concept too....?? how do we find the spread frm mean when there r many terms involved..??

Set A - {2, 4, ..., 100};
Set X - {-48, -46, ..., 50};
Set Y - {3, 6, ..., 150};
Set Z - {-2/4, -4/4, ..., -100/4} = {-1/2, -1, -3/2, ..., -25}.

If we add or subtract a constant to each term in a set the SD will not change, so sets A and X will have the same SD.

If we increase or decrease each term in a set by the same percent (multiply by a constant) the SD will increase or decrease by the same percent, so set Y will have 1.5 times greater SD than set A and set Z will have 4 times less SD than set A (note SD can not be negative so SD of Z wil be SD of A divided by 4 not by -4).

So, the ranking of SD's in descending order is: Y, A=X, Z.

Or the sane way as here: standard-deviation-110874.html#p890965

The standard deviation of a set shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.

You can see that set Y is most widespread and set Z is least widespread, so the correct answer is: Y, A=X, Z.

For more on SD check:
math-standard-deviation-87905.html
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Retired Moderator B
Joined: 16 Nov 2010
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Re: std deviation  [#permalink]

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The answer is D, I think the OA is wrongly posted as E.
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Manager  Joined: 05 Jul 2010
Posts: 125
Re: std deviation  [#permalink]

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it is D. See Bunuel's explaination.
Retired Moderator B
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Re: std deviation  [#permalink]

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Answer is D - Y,X,Z

For X - SD remains unchanged

For Y - SD is multiplied by 1.5

For Z - SD is divided by -4

OA given is wrong.
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Intern  Joined: 18 Jul 2013
Posts: 31
Re: Set A consists of all even integers between 2 and 100  [#permalink]

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Hi Bunnel,

Here in the question the arrangement asked is in descending order then why answer is D.

D option's arrangement is in ascending order isn't it.
Math Expert V
Joined: 02 Sep 2009
Posts: 58435
Re: Set A consists of all even integers between 2 and 100  [#permalink]

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taleesh wrote:
Hi Bunnel,

Here in the question the arrangement asked is in descending order then why answer is D.

D option's arrangement is in ascending order isn't it.

Y has the greatest SD, then comes X followed by Z, which has the least SD. So, Y, X, Z is in descending order.
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Intern  Joined: 18 Jul 2013
Posts: 31
Re: Set A consists of all even integers between 2 and 100  [#permalink]

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Hi Bunnel,

Thanks for the reply, i realized now it should be greater to smaller. Got confused, now it is clear.
Intern  Joined: 11 Jan 2016
Posts: 28
Re: Set A consists of all even integers between 2 and 100  [#permalink]

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So division (as in dividing every term in the set by the same number) makes the SD smaller, correct?

I understand the problem and what concepts apply but was lost when it came to division and SD.
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Re: Set A consists of all even integers between 2 and 100  [#permalink]

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gracie90 wrote:
So division (as in dividing every term in the set by the same number) makes the SD smaller, correct?

I understand the problem and what concepts apply but was lost when it came to division and SD.

Check out some posts on SD here:

https://www.veritasprep.com/blog/2012/0 ... deviation/
https://www.veritasprep.com/blog/2012/0 ... n-part-ii/
https://www.veritasprep.com/blog/2016/0 ... mula-gmat/
https://www.veritasprep.com/blog/2014/1 ... ion-on-sd/
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Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > Re: Set A consists of all even integers between 2 and 100   [#permalink] 14 Feb 2019, 21:05
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