If the mean of n observations ax1, ax2, ax3, ...., axn is aX show that (ax1-aX) + (ax2-aX) + .....+ (axn - aX) = 0

Explanation

Here sum of Observations = `ax1+ ax2 + ....... + axn`
No. of observations = `n`
Mean`(a bar X)=(ax1+ ax2 + ....... + axn)/n`


`n(a bar X)=ax1 + ax2 + ax3 + ..... + axn`.......(i)
LHS: `(ax1 -a bar X)+ (ax2-a bar X) + (ax3-a bar X) + ..... + (axn-a bar X)`
`(ax1+ax2+ax3+....axn)-(a bar X+ a bar X+...a bar X n`times)
`(ax1+ax2+ax3+....axn)-n a bar X`
`n(a bar X)-n a bar X =0`= RHS...from (i)
Hence proved