(i) To find the standard deviation, first determine the number of data points \(n\) using the equation for the mean:

\(\frac{133}{n} + 25 = 28.325\)

Solving for \(n\):

\(\frac{133}{n} = 3.325\)

\(n = 40\)

Next, use the formula for variance with coded data:

\(\frac{3762}{40} - 3.325^2 = 82.99\)

The standard deviation is:

\(\sqrt{82.99} = 9.11\)

(ii) To find \(\Sigma x^2\), use the uncoded variance formula:

\(82.99 = \frac{\Sigma x^2}{40} - 28.325^2\)

\(\Sigma x^2 = (82.99 + 28.325^2) \times 40\)

\(\Sigma x^2 = 35412\)

Alternatively, using the expanded form:

\(\Sigma(x - 25)^2 = \Sigma x^2 - 50\Sigma x + 40 \times 25^2\)

\(\Sigma x^2 = 3762 + 50 \times 1133 + 25000\)

\(\Sigma x^2 = 35412\)