The mean of a certain number of observations is x̄. If each observation is multiplied by m (m ≠ 0) and then increased by n, then the mean of new observations is :

1. $\Big(\dfrac{\bar x}{m} + n\Big)$

2. m $\bar x$ + n

3. m $\bar x$ − n

4. $\Big(\dfrac{\bar x}{m} - n\Big)$

Let the original observations be x₁, x₂, ……., x_k with a mean of $\bar{x}$.

The original mean is:

$\bar{x} = \dfrac{\sum x_i}{k}$

If every observation is multiplied by m, the new observations are, mx₁, mx₂,……., mx_k.

The sum of these new values is

$\sum mx$i = m(\sum xi).

Adding "n" to every term increases mean by "n":

$\text{Mean} = \dfrac{m(\sum x_i)}{k} = m \bar{x} + n$

Hence, option 2 is the correct option.