(i) Given the mean of the n values of x is 24.25, we have:

\(\frac{136}{n} + 20 = 24.25\)

Solving for \(n\):

\(24.25n - 20n = 136\)

\(4.25n = 136\)

\(n = \frac{136}{4.25} = 32\)

(ii) Using the coded information for variance:

\(\text{Variance} = \frac{2888}{32} - \left(\frac{136}{32}\right)^2\)

\(= 72.1875 \approx 72.19\)

Using the uncoded information for variance:

\(\text{Variance} = \frac{\Sigma x^2}{32} - 24.25^2\)

Equating the two expressions for variance:

\(\frac{\Sigma x^2}{32} - 24.25^2 = 72.1875\)

\(\frac{\Sigma x^2}{32} = 72.1875 + 24.25^2\)

\(\Sigma x^2 = 32 \times (72.1875 + 24.25^2)\)

\(\Sigma x^2 = 21128\)