In an experiment with 16 observations on $x$, the following results were obtained:
$\sum x = 182, \quad \sum x^2 = 3548$
One observation with value 20 was detected to be wrongly recorded and was replaced by its correct value 30. Find the corrected standard deviation. Answer ...

1. Correct the totals for the wrongly recorded value

Replace 20 with 30:
$\sum x = 182 - 20 + 30 = 192$
$\sum x^2 = 3548 - 20^2 + 30^2 = 3548 - 400 + 900 = 4048$

2. Compute the corrected mean and variance

With $n = 16$:
$\text{Mean} = \frac{192}{16} = 12$
$\text{Variance} = \frac{\sum x^2}{n} - \left(\frac{\sum x}{n}\right)^2 = \frac{4048}{16} - 12^2 = 253 - 144 = 109$

3. Find the standard deviation

$\sigma = \sqrt{109} = 10.44030\ldots \approx 10.4$