A set of data consists of the following 5 numbers: 0,2,4,6 and 8.Which two numbers,if added to create a set of 7 numbers will result in a new standard deviation that is close to the standard deviation for the original 5 numbers?
A.-1 and 9
B. 4 and 4
C. 3 and 5
D. 2 and 6
E. 0 and 8
My approach:
Though Not sure if a shorter method available but please advice if this one works!!
0 2 4 6 8 ..................mean ===>4
variance= ( X-m)^2 /N which is 2*(2^2+ 4^2)/5 = 8
now we need to add 2 numbers and be as close as posible to the original SD which is sqrt(8)
assume A as the sum of the new variances ....
A= (X6 - mean)^2 + (X7 - mean)^2
we know that
(40 + A)/7 = 8
(X6 - mean)^2 + (X7 - mean)^2= 16
(X6 - 4)^2 + (X7 - 4)^2 = 16
by looking into the choices..... i get from choice D ==>8
and from choice E ==> 32
both 32 and 8 are equidistant from 16
SO MY QUESTION IS WHICH ONE SHOULD I GO FOR :O
A.-1 and 9
B. 4 and 4
C. 3 and 5
D. 2 and 6
E. 0 and 8
My approach:
Though Not sure if a shorter method available but please advice if this one works!!
0 2 4 6 8 ..................mean ===>4
variance= ( X-m)^2 /N which is 2*(2^2+ 4^2)/5 = 8
now we need to add 2 numbers and be as close as posible to the original SD which is sqrt(8)
assume A as the sum of the new variances ....
A= (X6 - mean)^2 + (X7 - mean)^2
we know that
(40 + A)/7 = 8
(X6 - mean)^2 + (X7 - mean)^2= 16
(X6 - 4)^2 + (X7 - 4)^2 = 16
by looking into the choices..... i get from choice D ==>8
and from choice E ==> 32
both 32 and 8 are equidistant from 16
SO MY QUESTION IS WHICH ONE SHOULD I GO FOR :O
