Question

8.
The mean of n observations is x. If the first observation is
increased by 1. the second by 2. the third bý 3, and so on,
then the new mean is-
n ​

Answer 1

Answer:

The new mean is  $x+\frac{n+1}{2}$  .

Step-by-step explanation:

Given that the mean of $n$ observations is $x$. That is

$x=\dfrac{\text{sum of observations}}{n}$

Again, the first observation is increased by 1, the second observation by 2, and so on.

So there will be an increase in the sum of observations. The sum of the increase in observations is

Increase in the sum $=1+2+3+\cdots + n =\frac{n(n+1)}{2}$

Thus the new mean is,

$Mean = \dfrac{\text{Previous sum }+\text{ increase in sum}}{n} \\\\ \\ = \dfrac{\text{Previous sum }}{n}+\dfrac{n(n+1)}{2n} = x+\dfrac{n+1}{2}$

Hence the new mean is $x+\frac{n+1}{2}$  .