(i) To find the mean height \(\bar{x}\), use the formula:

\(\bar{x} = 130 - \frac{\Sigma(x - 130)}{82}\)

Substitute the given values:

\(\bar{x} = 130 - \frac{-287}{82} = 130 + \frac{287}{82}\)

\(\bar{x} = 130 + 3.5 = 126.5 \text{ cm}\)

(ii) To find \(\Sigma(x - 130)^2\), use the formula for variance:

\(\frac{\Sigma(x - 130)^2}{82} - (\bar{x} - 130)^2 = 6.9^2\)

Substitute \(\bar{x} - 130 = -3.5\):

\(\frac{\Sigma(x - 130)^2}{82} - (-3.5)^2 = 6.9^2\)

\(\frac{\Sigma(x - 130)^2}{82} = 6.9^2 + 3.5^2\)

\(\frac{\Sigma(x - 130)^2}{82} = 47.61 + 12.25 = 59.86\)

\(\Sigma(x - 130)^2 = 82 \times 59.86 = 4908.52\)

Thus, \(\Sigma(x - 130)^2 \approx 4908.5 \text{ cm}\).