Given: Mean of 20 values \(\bar{x} = 60\) and standard deviation \(s = 4\).

(i) To find \(\Sigma x\) and \(\Sigma x^2\):

\(\Sigma x = 60 \times 20 = 1200\)

\(Using the formula for variance:\)

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

\(4^2 = \frac{\Sigma x^2}{20} - 60^2\)

\(16 = \frac{\Sigma x^2}{20} - 3600\)

\(\frac{\Sigma x^2}{20} = 3616\)

\(\Sigma x^2 = 3616 \times 20 = 72320\)

(ii) For the combined 30 values:

\(\Sigma x = 1200 + 550 = 1750\)

\(\Sigma x^2 = 72320 + 40500 = 112800\)

Mean of 30 values:

\(\bar{x} = \frac{1750}{30} = 58.3\)

Variance of 30 values:

\(s^2 = \frac{112800}{30} - \left(\frac{1750}{30}\right)^2\)

\(s^2 = 3760 - 3412.89 = 357.11\)

Standard deviation:

\(s = \sqrt{357.11} \approx 18.9\)