The average of n numbers x₁, x₂.....x_n is $$\overline x $$ .Then the value of $$\sum\limits_{i\, = \,1}^n {} \left( {{x_i} - \overline x } \right)$$   is equal to -

According to the question,
Average of 'n' number's x₁, x₂.....x_n is $$\overline x $$
Sum of n numbers = n$${\overline x }$$
∴ $$\sum\limits_{i\, = \,1}^n {} \left( {{x_1} - \overline x } \right)$$
Put i = 1, 2, 3.....n then
{x₁ + x₂ + x₃ + .....(xn - n$${\overline x }$$)}
As we know that
x₁ + x₂ + x₃+.....+ x_nx = n$${\overline x }$$
= (n$${\overline x }$$ - n$${\overline x }$$)
= 0