Stunned by this question!!

[moneyman]

A certain list of 100 data has a mean of 6 and a standard deviation of d, where d is positive.Which of the following pairs of data, when added to the list, must result in a list 0f 102 data with std deviation less than d ?

-6 and 0
0 and 0
0 and 6
0 and 12
6 and 6

And also guys pls tell me how to post questions directly from the GMAT Prep window

[samirpandeyit62]

Hey this is very simple,

the stddev is the avg distance(seperation) of values in a distribution from the mean

so the values closest to mean here will result in decrease in the STD dev

E 6,6 is the closest i.e equal to mean so stddev will decrease as distance of these is 0. (i.e they make the distribution of the values closer to mean)

[gabriel]

A certain list of 100 data has a mean of 6 and a standard deviation of d, where d is positive.Which of the following pairs of data, when added to the list, must result in a list 0f 102 data with std deviation less than d ?

-6 and 0
0 and 0
0 and 6
0 and 12
6 and 6

And also guys pls tell me how to post questions directly from the GMAT Prep window

If I remember the formula for std. deviation correctly then the answer should be 6 and 6 ...

if there are 3 integers a,b,c and their mean is m .. then the std. deviation = root((m-a)^2+(m-b)^2+(m-c)^2)/3 (I am not entirely sure that i have got the formula right) ...

Now to the existing set of 100 integers if u add 6 and 6 the mean will remain the same .. 6 .. So while calculating the the std deviation the denominator will become 102, where as the numerator will remain the same because (6-6)^2=0 .. if the numerator remains the same and the denominator increases then the value of the fraction reduces .. so the answer should be 6 and 6 ... this is all under the assumption that my original formula for std. deviation is correct ..

[gabriel]

Grr .. Samir u beat me to the answer :twisted: .. I will let it slide this time



Regards

[samirpandeyit62]

Hey Gabriel, man u've already beaten the GMAT, I'm yet to do it, so I think u should give me some consideration

[gabriel]

Hey Gabriel, man u've already beaten the GMAT, I'm yet to do it, so I think u should give me some consideration

OK ... but only because your asking nicely 8) ...

Regards

[moneyman]

Thanks a lot for that simple explanation Samir!! This was the first question of the GMAT prep and I took nearly 5 mins to solve this considering the importance of the first 10 questions I guess I should stick to some logic and things will be much easier!!