If `barx_(1), barx_(2), barx_(3),………barx_(n)` are the means of n groups with `n_(1), n_(2), …………,n_(n)` number of observations, respectively, then the mean `barx` of all the groups taken together is given by

Options

A. `overset(n)underset(i=1)sumn_(i)overlinex_(i)`
B. `overset(n)underset(i=1)sum( n_(i)overlinex_(i))/(n^(2))`
C. `(sum_(i=1)^n ni barx_i)/(overset(n)underset(i=1)sum (n_(i))`
D. `overset(n)underset(i=1)sum (n_(i) overlinex_(i))/(2n)`

Answer

C

Explanation

sum of all terms = `n_(1)overlinex_(1) +n_(2)ovelinex_(2) +…..+x_(n)overlinex_(n)`
Number of terms = `n_(1)+n_(2) +……+n_(n)`
required mean = `(underset(i=1)overset(n)(sum)n_(i)x_(i))/(underset(i=1)overset(n)sum n_(i))`