(i) To find the mean speed, use the formula for the mean: \(\bar{x} = 60 + \frac{\Sigma(x - 60)}{70}\). Given \(\Sigma(x - 60) = 245\), we have:

\(\bar{x} = 60 + \frac{245}{70} = 60 + 3.5 = 63.5\)

(ii) To find \(\Sigma(x - 50)\), use the relationship:

\(\Sigma(x - 50) = \Sigma x - 70 \times 50\)

We know \(\Sigma(x - 60) = 245\), so:

\(\Sigma x = 245 + 70 \times 60\)

\(\Sigma x = 245 + 4200 = 4445\)

Then:

\(\Sigma(x - 50) = 4445 - 3500 = 945\)

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

\(\text{Variance} = \frac{\Sigma(x - 50)^2}{70} - \left(\frac{\Sigma(x - 50)}{70}\right)^2\)

Given the standard deviation is 10.6, the variance is \(10.6^2 = 112.36\).

Let \(\frac{\Sigma(x - 50)}{70} = 13.5\) (from part (ii)), then:

\(112.36 = \frac{\Sigma(x - 50)^2}{70} - 13.5^2\)

\(112.36 = \frac{\Sigma(x - 50)^2}{70} - 182.25\)

\(\frac{\Sigma(x - 50)^2}{70} = 112.36 + 182.25 = 294.61\)

\(\Sigma(x - 50)^2 = 294.61 \times 70 = 20623\)