Find the mean first=(1+1+5+5+8)/5=20/5=4.
Sum of squares of differences between each datum and the mean:
(1-4)2+(1-4)2+(5-4)2+(5-4)2+(8-4)2=9+9+1+1+16=36.
Divide by 5 to get the variance=36/5=7.2.
Standard deviation is the square root of the variance=√7.2=2.6833 approx. (=6/√5).