(iii) To find \(\Sigma(x - 60)^2\), calculate each \((x - 60)^2\) for the given times:
\((-15)^2, (-13)^2, (-7)^2, (-4)^2, (-4)^2, 1^2, 4^2, 6^2, 9^2, 13^2, 23^2, 15^2, 18^2\).
Summing these gives:
\(225 + 169 + 49 + 16 + 16 + 1 + 16 + 36 + 81 + 169 + 529 + 225 + 324 = 1856\).
Thus, \(\Sigma(x - 60)^2 = 1856\).
(iv) The variance is calculated using the formula:
\(\text{Var} = \frac{\Sigma(x - 60)^2}{n} - \left(\frac{\Sigma(x - 60)}{n}\right)^2\).
Given \(\Sigma(x - 60) = 46\) and \(n = 13\), substitute the values:
\(\text{Var} = \frac{1856}{13} - \left(\frac{46}{13}\right)^2\).
Calculate each part:
\(\frac{1856}{13} = 142.7692 \ldots\)
\(\left(\frac{46}{13}\right)^2 = 12.5385 \ldots\)
Thus, \(\text{Var} = 142.7692 - 12.5385 = 130.2307 \ldots \approx 130\).