Calculate the mean deviation about the mean of the set of first `n` natural numbers when `n` is even natural number.

Answer

N/a

Explanation

Consider first natural number when n is an odd ie.`1,2,3,4,…n ` [even ]
`therefore " Mean " bar x =(1+2+3+….+n)/(n) = (n(n+1))/(2n)= (n+1)/(2)`
` MD=(1)/(n)[abs(1-(n+1)/(2))+abs(2-(n+1)/2)+abs(3-(n+1)/2)]+abs((n-2)/(2)-(n+1)/(2))+abs(n/2-(n+1)/2)+abs((n+2)/(2)-(n+1)/(2))+...+abs(n-(n+1)/(2))`
`=1/n[abs((1-n)/(2))+abs((3-n)/2)+abs((5-n)/2)+.....+abs((-3)/2)+abs(1/2)+....+abs((n-1)/(2))]`
`(2)/(n)[(1)/(2)+(3)/2+.....+(n+1)/2](n/2)` terms
`=(1)/(n).(n/2)^2`
[`because` Sum of first n natural number `=n^(@)`]
`=(1)/(n).(n^(@)/4=n/4`