compute the population variance $sigma^{2}$ for the following sample data, assuming the sample comprises the…

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.\nx: 21 18 12 35 25\no 73.70\no 66.95\no 112.20\no 58.96\no 89.76

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.\nx: 21 18 12 35 25\no 73.70\no 66.95\no 112.20\no 58.96\no 89.76

Answer

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