First, calculate the mean \(\bar{x}\) using the formula:

\(\bar{x} = \frac{\Sigma x}{n} = \frac{645}{150} = 4.3\)

Next, use the formula for variance:

\(\text{Variance} = \frac{\Sigma x^2}{n} - \bar{x}^2 = \frac{8287.5}{150} - 4.3^2\)

Calculate \(\frac{8287.5}{150} = 55.25\) and \(4.3^2 = 18.49\).

Thus, the variance is:

\(55.25 - 18.49 = 36.76\)

The standard deviation is:

\(\sqrt{36.76} = 6.063\)

Finally, calculate \(\Sigma (x - \bar{x})^2\) using:

\(\Sigma (x - \bar{x})^2 = n \times \text{Variance} = 150 \times 36.76 = 5514\)

Rounding to the nearest whole number gives 5510.