Let the mean of 50 observations is 15 and the standard deviation is...

By using the formula of mean we get, $= \dfrac{∑ {x}_{i}}{50} = 15 ⇒ ∑ {x}_{i} = 750$

Now variance$= \dfrac{∑ {x}_{i}^{2}}{50} - {15}^{2} = {2}^{2} ⇒ ∑ {x}_{i}^{2} = 11450$

$⇒ \mathop{∑ {x}_{i}}_{\left(new\right)} = 50 \times 16 = 800$

So, $\mathop{∑ {x}_{i}}_{\left(new\right)} - ∑ {x}_{i} = 800 - 750 = 50$

Hence, if wrong observation was $x$ then corrected one is $x + 50$.
$⇒ x + \left(x + 50\right) = 70 ⇒ x = 10$

Therefore, the correct observation $= 60$.

Now, $\mathop{∑ {{x}_{i}}^{2}}_{\left(new\right)} = 11450 - {\left(10\right)}^{2} + {\left(60\right)}^{2} = 14950$

Therefore, variance of the correct set $= \dfrac{14950}{50} - {\left(16\right)}^{2} = 299 - 256 = 43$.