Question

if x bar is the arithmetic mean of n observations x1,x2,x3,.....,xn,then find the value of (x1-xbar)+(x2-xbar）+(xn-xbar）

Answer 1

Hope it helps.
Pl. mark as brainliest.

Answer 2

Answer:

The answer is 0.

Step-by-step explanation:

Given $\bar{x}$ is the arithmetic mean of n observations $x_1,x_2,...x_n$.

we have to find the value of $(x_1-\bar{x})+(x_2-\bar{x})+...+(x_n-\bar{x})$

Now,

$\bar{x}=\frac{x_1+x_2+x_3+....+x_n}{n}$

⇒ $n\bar{x}=(x_1+x_2+...+x_n)$  →    (1)

We have to find the value of

$(x_1-\bar{x})+(x_2-\bar{x})+....+(x_n-\bar{x})$

$=(x_1+x_2+....x_n)-n\bar{x}$

Using (1), we get

$=n\bar{x}-n\bar{x}\\\\=0$