Question

If x bar is the arithmetic mean of n observations x1,x2,x3,..........xn, then find the arithmetic mean of x1+a, x2+a, xn+a.
Pls answer it fast........

Answer 1

X bar is the arithmetic mean so

X bar=x1+x2+...........+xn/n

Adding a on both sides

X bar+a=x1+a+x2+a........xn+a/n

So the answer is X bar + a

Answer 2

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

We have to find mean of $x_1 + a, \:x_2 + a,\: .........x_n+a$

We know that, mean = (sum of observations)/(total number of observations)

So, mean = $\frac{x_1+a+x_2+a...x_n+a}{n}$

Here, total observations is n, and a is added to them n times, so we can write

mean

= $\frac{x_1+x_2....+x_n + a\times n}{n}$

$\implies\frac{x_1+x_2 ....+x_3}{n} + \frac{a\times n}{n}$

$\implies\overline{x} + a$

$(\texttt{since,}\frac{x_1+x_2...x_3}{n} = \overline{x})$

Hence, the new mean would be equal to the original mean + a