(i) The formula for the standard deviation \(\sigma\) is:

\(\sigma^2 = \frac{\Sigma (x-c)^2}{n} - \left(\frac{\Sigma (x-c)}{n}\right)^2\)

Given \(\sigma = 3.2\), \(n = 40\), and \(\Sigma (x-c)^2 = 3099.2\), we have:

\(3.2^2 = \frac{3099.2}{40} - \left(\frac{\Sigma (x-c)}{40}\right)^2\)

\(10.24 = 77.48 - \left(\frac{\Sigma (x-c)}{40}\right)^2\)

\(\left(\frac{\Sigma (x-c)}{40}\right)^2 = 67.24\)

\(\Sigma (x-c) = 40 \times \sqrt{67.24} = 328\)

(ii) Given \(c = 50\), the mean \(\bar{x}\) is:

\(\Sigma x - 40c = 328\)

\(\Sigma x = 328 + 40 \times 50 = 2328\)

\(\text{Mean} = \frac{2328}{40} = 58.2\)