Question

if x is the mean of x₁ , x₂ , ...... xₙ. prove that Σ( xi - x = 0)

Answer 1

YᎾᏌᎡ ᏚᎾᏞᏌᎢᏆᎾN -:

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Given :-

Mean of x1 , x2 , ....... xn..numbers is 'x'.

Prove -:

Σxi - x = 0

We know that,

Mean = sum of observations / number of observations.

x = x1 + x2 +..... xn / n

On cross multiplying,

nx = x1 + x2 +.... xn

Now,

= nΣxi - x = (x1 - x) + (x2 - x) +.......(xn - x)

= (x1 + x2 +......xn) - nx

= nx - nx

= 0

So, ∑xi - x= 0