(i) To find the mean, use the formula:

\(\text{Mean} = 45 + \frac{-148}{36} = 40.9\)

To find the variance, use:

\(\text{Var} = \frac{3089}{36} - \left(\frac{-148}{36}\right)^2 = 68.9\)

The standard deviation is:

\(\text{sd} = \sqrt{68.9} = 8.30\)

(ii) With the new data value of 29 added:

New \(\Sigma(x - 45) = -148 + (29 - 45) = -164\)

New \(\Sigma(x - 45)^2 = 3089 + (29 - 45)^2 = 3345\)

The new standard deviation is:

\(\text{New sd} = \sqrt{\frac{3345}{37} - \left(\frac{-164}{37}\right)^2} = 8.41\)