(i) To find \(\Sigma(x - 50)\), use the formula:

\(\Sigma(x - 50) = \Sigma x - 16 \times 50 = 824 - 800 = 24\)

To find \(\Sigma(x - 50)^2\), use the variance formula:

\(\frac{\Sigma(x - 50)^2}{16} - \left(\frac{\Sigma(x - 50)}{16}\right)^2 = 6.5^2\)

\(\frac{\Sigma(x - 50)^2}{16} - \left(\frac{24}{16}\right)^2 = 42.25\)

\(\Sigma(x - 50)^2 = 712\)

(ii) With the new mark, the total sum becomes \(824 + 72 = 896\) and the number of students is 17.

New mean:

\(\text{New mean} = \frac{896}{17} = 52.7\)

New variance:

\(\text{New variance} = \frac{712 + 22^2}{17} - \left(\frac{24 + (72 - 50)}{17}\right)^2\)

\(= \frac{712 + 484}{17} - \left(\frac{46}{17}\right)^2\)

\(= \frac{1196}{17} - \left(2.7059\right)^2\)

\(= 70.3529 - 7.3248 = 63.0281\)

New standard deviation:

\(\text{New standard deviation} = \sqrt{63.0281} \approx 7.94\)