First, calculate the average (you might want a calculator):
#x={13, 11, 4, 5, 6, 9, 10, 12, 15, 16}#
#barx=(13+11+4+5+6+9+10+12+15+16)/10#
#color(white)barx=101/10#
#color(white)barx=10.1#
Using the standard deviation formula:
#sigma=sqrt((sum_(i=1)^(n) (x_i-barx)^2)/n)#
We can plug in our values:
#sigma=sqrt((sum_(i=1)^(10) (x_i-10.1)^2)/10)#
#color(white)sigma=sqrt(((13-10.1)^2+(11-10.1)^2+(4-10.1)^2+(5-10.1)^2+(6-10.1)^2+(9-10.1)^2+(10-10.1)^2+(12-10.1)^2+(15-10.1)^2+(16-10.1)^2)/10)#
#color(white)sigma=sqrt((2.9^2+0.9^2+(-6.1)^2+(-5.1)^2+(-4.1)^2+(-1.1)^2+(-0.1)^2+1.9^2+4.9^2+5.9^2)/10)#
#color(white)sigma=sqrt((8.41+0.81+37.21+26.01+16.81+1.21+0.01+3.61+24.01+34.81)/10)#
#color(white)sigma=sqrt(152.9/10)#
#color(white)sigma=sqrt(15.29)#
#color(white)sigma~~3.9102...#
