We start with the equation \(\Sigma(x - 36) = -60\). Expanding this gives:

\(\Sigma x - 24 \times 36 = -60\)

\(\Sigma x = 24 \times 36 - 60 = 804\)

Next, we use \(\Sigma(x - 36)^2 = 227.76\). Expanding gives:

\(\Sigma x^2 - 2 \times 36 \times \Sigma x + 24 \times 36^2 = 227.76\)

Substitute \(\Sigma x = 804\):

\(\Sigma x^2 - 2 \times 36 \times 804 + 24 \times 1296 = 227.76\)

\(\Sigma x^2 - 57888 + 31104 = 227.76\)

\(\Sigma x^2 = 227.76 + 57888 - 31104 = 27011.76\)