Question

the mean of n observations x1,x2,x3.........xn is x bar. if each observation is decreased by p, then show that the mean of the new observations is {x bar-p}

Answer 1

Answer:

The proof is explained below.

Step-by-step explanation:

Given the mean of n observations $x_1,x_2,x_3,...x_n$ is x bar.

Now, if each observation is decreased by p. we have to show that the mean of the new observations is {x bar-p}.

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

Now, each observation is decreased by p i.e

$x_1-p, x_2-p, x_3-p,...x_n-p$

Mean can be calculated as

$Mean=\frac{(x_1-p)+(x_2-p)+(x_3-p)+.....+(x_n-p)}{n}$

         $=\frac{x_1+x_2+x_3+.....+x_n}{n}-\frac{np}{n}$

         $=\bar{x}-p$

Hence proved.