Question

if x bar is mean of n observations x1 x2 x3 x4.............xn then find sigma { x - xbar}??

Answer 1

$\textsf{Given:}$

$\textsf{ x_1,\;x_2\;.....x_n are n observations}$

$\mathsf{Mean,\;\overline{x}=\displaystyle\frac{\Sigma{x_i}}{n}}$

$\mathsf{Mean,\;\overline{x}=\displaystyle\frac{x_1+x_2+x_3+.........+x_n}{n}}$

$\textsf{Now,}$

$\mathsf{\Sigma(x_i-\overline{x})}$

$\mathsf{=(x_1-\overline{x})+(x_2-\overline{x})+(x_3-\overline{x})+.........+(x_n-\overline{x})}$

$\mathsf{=(x_1+x_2+x_3+.........+x_n)-n\,\overline{x}}$

$\mathsf{=n\,\overline{x}-n\,\overline{x}}$

$\mathsf{=0}$

$\implies\boxed{\mathsf{\Sigma(x_i-\overline{x})=0}}$

Answer 2

Answer:

0

Step-by-step explanation:

given:

\textsf{$x_1,\;x_2\;.....x_n$ are n observations}x

1

,x

2

.....x

n

are n observations

\mathsf{Mean,\;\overline{x}=\displaystyle\frac{\Sigma{x_i}}{n}}Mean,

x

=

n

Σx

i

\mathsf{Mean,\;\overline{x}=\displaystyle\frac{x_1+x_2+x_3+.........+x_n}{n}}Mean,

x

=

n

x

1

+x

2

+x

3

+.........+x

n

\textsf{Now,}Now,

\mathsf{\Sigma(x_i-\overline{x})}Σ(x

i

−

x

)

\mathsf{=(x_1-\overline{x})+(x_2-\overline{x})+(x_3-\overline{x})+.........+(x_n-\overline{x})}=(x

1

−

x

)+(x

2

−

x

)+(x

3

−

x

)+.........+(x

n

−

x

)

\mathsf{=(x_1+x_2+x_3+.........+x_n)-n\,\overline{x}}=(x

1

+x

2

+x

3

+.........+x

n

)−n

x

\mathsf{=n\,\overline{x}-n\,\overline{x}}=n

x

−n

x

\mathsf{=0}=0

\implies\boxed{\mathsf{\Sigma(x_i-\overline{x})=0}}⟹

Σ(x

i

−

x

)=0