Question

compute the value of sigma(fixi-x bar) for n observations.​

Answer 1

GIVEN :

The expression $\sum(f_ix_i-\overline{X})$ for n observations

TO FIND :

The value of the expression $\sum(f_ix_i-\overline{X})$ for n observations

SOLUTION :

Given that total number of observations is n

Let mean of n observations be $\overline{X}$

then $\frac{(x_1 +x_2 +x_3 +...+x_n )}{n} =\overline{X}$

$x_1 +x_2 +x_3 +...+x_n= n\times \overline{X}$

Now $\sum (x_i - \overline{X}) = {(x_1 -\overline{X}) + (x_2 -\overline{X}) + (x_3 -\overline{X})+...+(x_n -\overline{X})} - n\times \overline{X}$

$= (x_1 +x_2 +x_3 +...+x_n ) - n\times \overline{X}$

$= n\times \overline{X} - n\times \overline{X}$

 = 0

∴ $\sum (x_i - \overline{X})=0$

∴ The value of  $\sum (f_ix_i - \overline{X})$ is 0