These data show the ring sizes for a sample of 8 men. 12 10 11.5 11.5 12 9 9 11 What is the best approximation of the standard deviation for the ring size data?

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