Question

If x is the mean of the ten natural numbers `x_1, x_2 , x_3+....... + x_10` show that (x₁ -x) + (x₂ - x) +.........+ (x₁₀ - x)` = 0 

Answer 1

We have , x = `( x_1 + x_2 +...... + x_10) / 10`

⇒ `x_1 +x_2 + ..........+ x_10 = 10barx  ..... (1)`

⇒ Now , `(x_1 - barx) + (x_2- barx)+.........+ (x_10 - barx)`

⇒ `10barx  - 10barx`       [By equation (1)]

∴ `(x_2- barx) + (x_2 - barx) +.......+ (x_10 - barx)`0 Hence proved.