A certain set of numbers has an average (arithmetic mean) of

Question

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

A. -200
B. -130
C. -104
D. 51
E. 305

Bunuel · Accepted Answer

2 standard deviations from the average is from mean - 2*SD to mean + 2*SD , thus from 50-2*50.5=51 to 50+2*50.5=151: -51 < m < 151 -51 < n < 151 -102 < m+n < 302. Only option D is in this range. Answer: D. Similar questions to practice: arithmetic-mean-and-standard-deviation-of-a-certain-normal-104117.html 70-75-80-85-90-105-105-130-130-130-the-list-shown-consist-of-100361.html for-a-certain-exam-a-score-of-58-was-2-standard-deviations-b-128661.html a-certain-characteristic-in-a-large-population-has-a-143982.html a-vending-machine-is-designed-to-dispense-8-ounces-of-coffee-93351.html the-residents-of-town-x-participated-in-a-survey-83362.html the-standard-deviation-of-a-normal-distribution-of-data-is-99221.html the-mean-and-the-standard-deviation-of-the-8-numbers-shown-98248.html the-lifetime-of-all-the-batteries-produced-by-a-certain-comp-101472.html the-standard-deviation-of-a-normal-distribution-of-data-is-99221.html Hope this helps.

adg142000 · Answer

mean is 50 and SD 50.5 ,, so the nos are between 50-50.5 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

Bunuel · Answer

The numbers are 2 standard deviations from the average, not 1 standard deviation.

jabgars · Answer

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?

Bunuel · Answer

No, constructing a set is a bad way to solve this question. It has MUCH easier solution.

pacifist85 · Answer

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...

ScottTargetTestPrep · Answer

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

Kinshook · Answer

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

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A certain set of numbers has an average (arithmetic mean) of

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