If the mean of the observations a, a + 6, a + 2, a + 8 and a + 4 is 11, find :
(i) the value of 'a'
(ii) the median

Options

A. `(n(n+1))/2d^2`
B. `(n(n+1))/3d^2`
C. `(n(n+1))/6d^2`
D. `(n(n+1))/12d^2`

Answer

B

Explanation

Given series a,a+d,a+2d,…., a+2nd
`barx=(((2n+1)/2)(a+a+2nd))/(2n+1)=a+nd`
`Sigma(x_i-barx)^2=n^2 d^2 + (1-n)^2 d^2` +….+ `d^2+0+d^2`+….+`n^2d^2`
`=2d^2 (n^2+(n-1)^2+….+1^2)=(n(n+1)(2n+1))/3 d^2`
`therefore` Variance =`(Sigma(x_i-barx)^2)/(2n+1)=(n(n+1))/3 d^2`