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A certain set of numbers has an average (arithmetic mean) of
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Updated on: 21 Oct 2013, 21:01
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A certain set of numbers has an average (arithmetic mean) of 50 and a standard deviation of 50.5. If m and n, two numbers in the set, are both within 2 standard deviations from the average, then which of the following could be the sum of m and n? A. 200 B. 130 C. 104 D. 51 E. 305
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Originally posted by jabgars on 21 Oct 2013, 19:13.
Last edited by Bunuel on 21 Oct 2013, 21:01, edited 2 times in total.
Renamed the topic and edited the question.




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Re: A certain set of numbers has an average (arithmetic mean) of
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21 Oct 2013, 21:11




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21 Oct 2013, 19:42
jabgars wrote: A certain set of numbers has an average (arithmetic mean) of 50 and a standard deviation of 50.5. If m and n, two numbers in the set, are both within 2 standard deviations from the average, then which of the following could be the sum of m and n? 200 130 104 51 305 mean is 50 and SD 50.5 ,, so the nos are between 5050.5 and 50+50.5 i,e 0.5 and 100.5 ,, so the nos from the option which will be sum of m and n in range is 51 which is the answer



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Re: The Economist:GMAT tutor Quantitative Section
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21 Oct 2013, 21:13
adg142000 wrote: jabgars wrote: A certain set of numbers has an average (arithmetic mean) of 50 and a standard deviation of 50.5. If m and n, two numbers in the set, are both within 2 standard deviations from the average, then which of the following could be the sum of m and n? 200 130 104 51 305 mean is 50 and SD 50.5 ,, so the nos are between 5050.5 and 50+50.5 i,e 0.5 and 100.5 ,, so the nos from the option which will be sum of m and n in range is 51 which is the answer The numbers are 2 standard deviations from the average, not 1 standard deviation.
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Re: A certain set of numbers has an average (arithmetic mean) of
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23 Oct 2013, 18:04
Thanks for explaining the answer guys. Did you ever consider trying to pick a few numbers and guessing based on that? I got stuck when I thought about picking numbers since the question never gives us the information on the number of values in the set. Say for example, I pick 5/25/50/75/95, my average is 50 but my standard deviation is way off than 50.5 but still is there a way to figure this out with numbers?



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Re: A certain set of numbers has an average (arithmetic mean) of
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23 Oct 2013, 23:24
jabgars wrote: Thanks for explaining the answer guys. Did you ever consider trying to pick a few numbers and guessing based on that? I got stuck when I thought about picking numbers since the question never gives us the information on the number of values in the set. Say for example, I pick 5/25/50/75/95, my average is 50 but my standard deviation is way off than 50.5 but still is there a way to figure this out with numbers? No, constructing a set is a bad way to solve this question. It has MUCH easier solution.
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Re: A certain set of numbers has an average (arithmetic mean) of
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14 Jan 2015, 03:44
First, let me give one way to see the SD on a number line, because if someone gets confused by more than 1 SD, this is helful:
M= mean SD= standard deviation
___3SD___2SD___1SD___M___+1SD___+2SD___+3SD___ This is the number line showing M and up to 3SD. _____7______8______9____10____11______12_____13____ Here I added numbers for M=10 and 1SD=1
They way I solved it was by adding m+n, based on the values they could receive, like this: m=151 (+2SD) m=51 (2SD) n=151 (+2SD) n=51 (2SD), so each number could be either +2SD from the mean or 2SD from the mean.
In other words: m+n= 151+151 = 302 m+n= 51+(51) = 0 m+n= 151+(51) = 100 m+n= 51+151 = 100
And the range seems to be: 0<m+n<302
Only D is in this range. ANS D
I hope I didn't make any mistakes...



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Re: A certain set of numbers has an average (arithmetic mean) of
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08 Sep 2019, 05:54
jabgars wrote: A certain set of numbers has an average (arithmetic mean) of 50 and a standard deviation of 50.5. If m and n, two numbers in the set, are both within 2 standard deviations from the average, then which of the following could be the sum of m and n?
A. 200 B. 130 C. 104 D. 51 E. 305 Two standard deviations below the mean of 50 is 50  2*(50.5) = 50  101 = 51, and two standard deviations above 50 is 50 + 2*(50.5) = 50 + 101 = 151. Thus, we have 51 < m, n < 151. We see that m + n must be greater than 2*(51) = 102 and less than 2*151 = 302. Thus, all answer choices besides D are eliminated. Indeed, we can pick m = 0 and n = 51 so that m + n = 51. Answer: D
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A certain set of numbers has an average (arithmetic mean) of
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08 Sep 2019, 06:23
jabgars wrote: A certain set of numbers has an average (arithmetic mean) of 50 and a standard deviation of 50.5. If m and n, two numbers in the set, are both within 2 standard deviations from the average, then which of the following could be the sum of m and n?
A. 200 B. 130 C. 104 D. 51 E. 305 Given: A certain set of numbers has an average (arithmetic mean) of 50 and a standard deviation of 50.5. Asked: If m and n, two numbers in the set, are both within 2 standard deviations from the average, then which of the following could be the sum of m and n? Range of m = 50 + 2*50.5 = 151 or 51 Range of n = 50 + 2*50.5 = 151 or 51 51<{m,n} <151 102<m+n<302 Only D 51 satisfies the conditions IMO D




A certain set of numbers has an average (arithmetic mean) of
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08 Sep 2019, 06:23






