Let q be the range and `S^(2)=(1)/(n-1) underset(i=1)overset(n)sum (x_(i)-x)^(2)` be the S.D. of a set of observations `x_(1),x_(2),........,x_(n)`. Then

If sum_(i=1)^(10)(x_(i)-15)=12 and sum_(i=1)^(10)(x-15)^(2)=18 then the S.D.of observation x_(1),x_(2),x_(3),....x_(10) is:

If n is a positive integer and if (1+x+x^(2))^(2n)=underset(r=0)overset(2n)(sum)a_(r)x^(r) , then

If the mean and S.D. of n observations x_(1),x_(2)......x_(n) are x and ? resp,then the sum of squares of observations is

If the mean of a set of observations x_(1),x_(2), …,x_(n)" is " bar(X) , then the mean of the observations x_(i) +2i , i=1, 2, ..., n is

If the standard deviation of n observation x_(1), x_(2),…….,x_(n) is 5 and for another set of n observation y_(1), y_(2),………., y_(n) is 4, then the standard deviation of n observation x_(1)-y_(1), x_(2)-y_(2),………….,x_(n)-y_(n) is

If f(x) = (a^(x))/(a^(x) + sqrt(a)), a gt 0 prove that (i) f(x) + f(1-x) = 1 (ii) underset(k=1)overset(2n-1)sum 2f ((k)/(2n)) = 2n-1 (iii) underset(k=1)overset(2n)sum 2f((k)/(2n+1)) = 2n