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mean median concept explain please :)

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by divya23 » Fri Jun 10, 2011 5:35 pm
A certain list of 100 data has mean of 6 and S.D = d and d = +ve ..Which of the following pairs of data when added to the list must result in a list of 102 data with s.d < d.
-6 and 0
0 and 0
0 and 6
0 and 12
6 and 6

oa 5

i got this question right but i want to know if the formula or the method that i applied is correct or not ..somebody please explain me this concept
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by cans » Fri Jun 10, 2011 5:55 pm
mean=6
s.d. = d
n=100 (no. of elements)
to decrease the s.d. of new set, the elements must be added close to the mean)
e)6&6 will keep mean same as 6 and also thus standard deviation will decrease.
IMO E
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by divya23 » Fri Jun 10, 2011 6:05 pm
what is the formula for this??
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by pemdas » Fri Jun 10, 2011 7:06 pm
attached is the formula of s.d.

n can be 100 or 102

as you see the '0' effect on numerator of s.d. is achieved by the pair 6,6
and the n is increasing, n=102. Hence s.d. will be less than d, as in the numerator of s.d. all numbers are squared and may be greater than d.
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