The Variance:
(12+6+8+5+2+7+3+5+6+7)/10=6.1 is mean (average)
Then you subtract 6.1 from each number in the data set and after getting the result you do the same thing as finding the average but you also have to square the result. So:
(5.9^2+(-0.1)^2+1.9^2+(-1.1)^2+(-4.1)^2+0.9^2+(-3.1)^2+(-1.1)^2+(-0.1)^2+0.9^2)/10= 6.89
Variance is 6.89.
Standard Deviation is just the square root of Variance, so:
√6.89=2.62 (the answer is rounded)