The mean and standard deviation of 10 observations are 20 and 8...

Incorrect mean is

$\dfrac{\mathop{∑}_{i = 1}^{10}{x}_{i}}{10} = 20$

$⇒ \mathop{∑}_{i = 1}^{10}{x}_{i} = 200 . . . . \left(i\right)$

So, corrected mean is

$\dfrac{\mathop{∑}_{i = 1}^{10}{x}_{i} - 50 + 40}{10} = \dfrac{200 - 10}{10} = 19$

Incorrect variance is

$\dfrac{\mathop{∑}_{i = 1}^{10}{x}_{i}^{2}}{10} - 400 = 64$

$⇒ \mathop{∑}_{i = 1}^{10}{x}_{i}^{2} = 4640$

Now, corrected variance is

$= \dfrac{\mathop{∑}_{i = 1}^{9}{x}_{i}^{2} + {40}^{2} - {50}^{2}}{10} - {\left(19\right)}^{2}$

$= \dfrac{4640 - 900}{10} - {\left(19\right)}^{2} = 374 - 361 = 13$