The population size of the above data is 8, that is N=8
The mean (average) = (12 +10+ 11.5 +11.5 +12 +9 +9 +11)/8
= 10.75
Standard deviation is the square root of variance, it is one of the measures of central dispersion, that is a measure of by how much the values in the data set are likely to differ from the mean.
In this case, Standard deviation, s= √(∑(x-m)²)/(n-1)
= 1.172
Thus, best approximation of the standard deviation is 1.17