The mean of $x_1, x_2, x_3, ……, x_n$ is $m$. The value of each variate is increased by 2. The mean of the new data is:

Given,

Mean of $x_1, x_2, x_3, ……, x_n$ = $m$

$\Rightarrow \frac{x_1 + x_2 + \dots + x_n}{n} = m$

When each variate is increased by 2, the new mean is:

$$\begin{aligned}\Rightarrow \frac{(x_1 + 2) + (x_2 + 2) + \dots + (x_n + 2)}{n} \\[1em] \Rightarrow \frac{(x_1 + x_2 + \dots + x_n) + 2n}{n} \\[1em] \Rightarrow \frac{x_1 + x_2 + \dots + x_n}{n} + \frac{2n}{n} \\[1em] \Rightarrow m + 2.\end{aligned}$$

Hence, option 3 is the correct option.