If x bar is the mean of x1,x2 ,x3 ,x4 ,x5 then prove that (x1-x bar)+(x2-x bar)+(x3-xbar)+(x4-x bar)+(x5-xbar)=0 - Maths - Statistics

Question

If x bar is the mean of x1,x2 ,x3
,x4 ,x5
then prove that
(x1-x bar)+(x2-x
bar)+(x3-xbar)+(x4-x
bar)+(x5-xbar)=0

Pronay · Accepted Answer

$\bar{x} = \frac{x_{1} + x_{2} + x_{3} + x_{4} + x_{5}}{5}$

$(x_{1} - \bar{x}) + (x_{2} - \bar{x}) + (x_{3} - \bar{x}) + (x_{4} - \bar{x}) + (x_{5} - \bar{x}) = (x_{1} + x_{2} + x_{3} + x_{4} + x_{5}) - 5 \bar{x} = 5 \bar{x} - 5 \bar{x} = 0$