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Set A consists of all even integers between 2 and 100
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Updated on: 17 Jul 2012, 03:34
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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
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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.




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Re: std deviation
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14 Mar 2011, 10:12
punyadeep wrote: 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. Answer: D. Or the sane way as here: standarddeviation110874.html#p890965The 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. Answer: D. For more on SD check: mathstandarddeviation87905.htmldsquestionsaboutstandarddeviation85896.htmlpsquestionsaboutstandarddeviation85897.html
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Re: std deviation
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14 Mar 2011, 19:28
The answer is D, I think the OA is wrongly posted as E.
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Re: std deviation
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17 Apr 2011, 13:51
it is D. See Bunuel's explaination.



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Re: std deviation
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17 Apr 2011, 19:06
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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Re: Set A consists of all even integers between 2 and 100
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20 Aug 2014, 16:18
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.



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Re: Set A consists of all even integers between 2 and 100
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21 Aug 2014, 04:00
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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Re: Set A consists of all even integers between 2 and 100
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21 Aug 2014, 09:17
Hi Bunnel,
Thanks for the reply, i realized now it should be greater to smaller. Got confused, now it is clear.



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Re: Set A consists of all even integers between 2 and 100
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02 Dec 2016, 05:02
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
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14 Feb 2019, 21:05
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 ... npartii/https://www.veritasprep.com/blog/2016/0 ... mulagmat/https://www.veritasprep.com/blog/2014/1 ... iononsd/
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Re: Set A consists of all even integers between 2 and 100
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14 Feb 2019, 21:05






