First, calculate \(\Sigma x\) using the given \(\Sigma(x - 20) = 35\):

\(\Sigma x - 50 \times 20 = 35\)

\(\Sigma x = 35 + 1000 = 1035\)

Now, find the mean \(\bar{x}\):

\(\bar{x} = \frac{\Sigma x}{50} = \frac{1035}{50} = 20.7\)

Use the formula for variance:

\(\text{Variance} = \frac{\Sigma x^2}{50} - \left(\frac{\Sigma x}{50}\right)^2\)

Substitute the values:

\(\text{Variance} = \frac{25036}{50} - \left(\frac{1035}{50}\right)^2\)

\(\text{Variance} = 500.72 - (20.7)^2\)

\(\text{Variance} = 500.72 - 428.49\)

\(\text{Variance} = 72.23\)