If M is the mean of x 1 , x 2 , x 3 , x 4 , x 5 and x 6 , prove that ( x 1 - M )+ ( x 2 - M )+ ( x 3 - M )+ ( x 4 - M )+ ( x 5 - M )+( x 6 - M ) = 0.

Question

Philoid · Accepted Answer

Let M is the mean of x₁, x₂, x₃, x₄, x₅ and x₆

Then, M =

6M = x₁ + x₂ + x₃ + x₄ + x₅ + x₆

To prove: (x₁-M) + (x₂-M) + (x₃-M) + (x₄-M) + (x₅-M) + (x₆-M) = 0

Proof: L.H.S

= (x₁ – M) + (x₂ – M) + (x₃ + M) + (x₄ – M) + (x₅ – M) + (x₆ – M)

= (x₁ + x₂ + x₃ + x₄ + x₅ + x₆) – (M+ M + M + M + M + M)

= 6M – 6M

= 0

= R.H.S