(a) The mean of the 40 values of \(x\) is given by:

\(\frac{\Sigma x}{40} = 34\)

We know \(\Sigma(x-k) = 520\), so:

\(\frac{\Sigma x - 40k}{40} = \frac{520}{40}\)

\(34 - k = 13\)

\(k = 34 - 13 = 21\)

(b) The variance is calculated using:

\(\text{Var} = \frac{\Sigma(x-k)^2}{40} - \left(\frac{\Sigma(x-k)}{40}\right)^2\)

Substitute the given values:

\(\text{Var} = \frac{9640}{40} - \left(\frac{520}{40}\right)^2\)

\(\text{Var} = 241 - 13^2\)

\(\text{Var} = 241 - 169 = 72\)