Official solution
Mean = \[{{6 + 10 + 7 + 13 + a + 12 + b + 12} \over 8} = 9\]
60 + a + b = 72
a + b = 12 .....(1)
variance \[ = {{\sum {x_i^2} } \over n} - {\left( {{{\sum {x_i^{}} } \over n}} \right)^2} = {{37} \over 4}\]
\[\sum {x_i^2} = {6^2} + {10^2} + {7^2} + {13^2} + {a^2} + {b^2} + {12^2} + {12^2} = {a^2} + {b^2} + 642\]
\[{{{a^2} + {b^2} + 642} \over 8} - {(9)^2} = {{37} \over 4}\]
\[{{{a^2} + {b^2}} \over 8} + {{321} \over 4} - 81 = {{37} \over 4}\]
\[{{{a^2} + {b^2}} \over 8} = 81 + {{37} \over 4} - {{321} \over 4}\]
\[{{{a^2} + {b^2}} \over 8} = 81 - 71\]
\[\therefore\] a2 + b2 + 2ab = 144
80 + 2ab = 144
\[\therefore\] 2ab = 64
\[ \therefore \] \[{(a - b)^2} = {a^2} + {b^2} - 2ab = 80 - 64 = 16\]