Question

compute the population variance $sigma^{2}$ for the following sample data, assuming the sample comprises the entire population. round your answer to the nearest hundredth.
x: 21 18 12 35 25
o 73.70
o 66.95
o 112.20
o 58.96
o 89.76

Explanation:

Step1: Calculate the mean

$\bar{x}=\frac{21 + 18+12+35+25}{5}=\frac{111}{5}=22.2$

Step2: Calculate the squared - differences

$(21 - 22.2)^2=(-1.2)^2 = 1.44$
$(18 - 22.2)^2=(-4.2)^2=17.64$
$(12 - 22.2)^2=(-10.2)^2 = 104.04$
$(35 - 22.2)^2=(12.8)^2=163.84$
$(25 - 22.2)^2=(2.8)^2 = 7.84$

Step3: Calculate the population variance

$\sigma^{2}=\frac{1.44 + 17.64+104.04+163.84+7.84}{5}=\frac{294.8}{5}=58.96$

Answer:

58.96