Question

For the following set of data, find the standard deviation (to the nearest hundredth): (1, 2, 2, 4, 5, 5, 5, 6)

Answer 1

x = (1,2,2,4,5,5,5,6)
n = 8
Calculate the mean.
m = (1+2+2+4+5+5+5+6)/8 = 3.75
x-m = (-2.75, -1.75, -1.75, 0.25, 1.25, 1.25, 1.25, 2.25)
(x-m)^2 = (7.5625, 3.0325, 3.0625, 0.0625, 1.5625, 1.5625, 1.5625, 5.0625)

Calculate std. deviation.
$s = \sqrt{\frac{(x-m)^2}{(n-1)}} = \sqrt{\frac{23.5}{7}} = 1.8323$

Answer: 1.8323