First, calculate \(\Sigma(x - 10)\):

\(\Sigma(x - 10) = \Sigma x - 12 \times 10 = 186 - 120 = 66\)

Next, use the formula for variance to find \(\Sigma(x - 10)^2\):

Given the standard deviation \(\sigma = 4.5\), the variance is \(\sigma^2 = 4.5^2 = 20.25\).

The formula for variance is:

\(\frac{\Sigma(x - 10)^2}{12} - \left(\frac{\Sigma(x - 10)}{12}\right)^2 = 20.25\)

Substitute \(\Sigma(x - 10) = 66\):

\(\frac{\Sigma(x - 10)^2}{12} - \left(\frac{66}{12}\right)^2 = 20.25\)

\(\frac{\Sigma(x - 10)^2}{12} - 5.5^2 = 20.25\)

\(\frac{\Sigma(x - 10)^2}{12} - 30.25 = 20.25\)

\(\frac{\Sigma(x - 10)^2}{12} = 50.5\)

\(\Sigma(x - 10)^2 = 606\)