Given $$\overline x = 15,\,\sigma = 2 \Rightarrow {\sigma ^2} = 4$$

$$\therefore$$ $${x_2} + {x_2} + \,\,.....\,\, + \,\,{x_{50}} = 15 \times 50 = 750$$

$$4 = {{x_1^2 + x_2^2 + \,\,.....\,\, + \,\,x_{50}^2} \over {50}} - 225$$

$$\therefore$$ $$x_1^2 + x_2^2 + \,\,.....\,\, + \,\,x_{50}^2 = 50 \times 229$$

Let a be the correct observation and b is the incorrect observation

then $$a + b = 70$$

and $$16 = {{750 - b + a} \over {50}}$$

$$\therefore$$ $$a - b = 50 \Rightarrow a = 60,\,b = 10$$

$$\therefore$$ Correct variance $$ = {{50 \times 229 + {{60}^2} - {{10}^2}} \over {50}} - 256 = 43$$