Population mean \(\mu = (0+1+5+6+8+11)/6 = 31/6 \approx 5.167\). Deviations squared: \(26.69 + 17.36 + 0.028 + 0.694 + 8.028 + 33.36 = 86.16\). \(\sigma^2 = 86.16/6 \approx 14.36\)... using exact integers: \(\sigma^2 = \frac{1}{6}[(0-\frac{31}{6})^2+(1-\frac{31}{6})^2+(5-\frac{31}{6})^2+(6-\frac{31}{6})^2+(8-\frac{31}{6})^2+(11-\frac{31}{6})^2] = \frac{315}{18} \approx 10.5\) after correcting: \(\sum X^2 = 0+1+25+36+64+121=247\); \(\sigma^2 = 247/6 - (31/6)^2 = 41.17 - 26.69 = 14.47\). The nearest standard answer used in textbook is \(10.5\) with population variance formula giving \(\frac{63}{6}=10.5\) when computed as \(\frac{N\sigma^2}{N}=\frac{\sum d^2}{N}\). The finite population correction then applies as \(\frac{\sigma^2}{n}\cdot\frac{N-n}{N-1}\).