If the mean of `n` observation `a x_1, a x_2, a x_3, ,a x_n` is `a barX` , show that `(a x_1-a barX )+(a x_2-a barX )++(a x_n-a barX)=0`

Explanation

We have:
`abarx=(ax_1+ax_2+.........+ax_n)/n`
`ax_1+ax_2+.......+ax_n=n(abarx)` .................(i)
Now,
`(ax_1-abarx)+(ax_2-abarx)+...........+(ax_n-abarx)`
`=(ax_1+ax_2+........+ax_n)-(abarx+abarx+.......+abarx)`
Using (i),
`=n(abarx)-n(abarx=0`
Hencce Proved.