Answer to Question #342494 in Statistics and Probability for gwapo

Question #342494

A population consists of the elements 3, 5, 7, 8, and 10. What is the population variance?




Round off your answer to the nearest hundredths.

1
Expert's answer
2022-05-19T09:43:12-0400

Population mean:

"\\mu=\\cfrac{3+5+7+8+10}{5}=6.6."


Population variance:

"\\sigma^2=\\sum(x_i-\\mu)^2\\cdot P(x_i),"

"X-\\mu=\\\\\n=\\begin{Bmatrix}\n 3-6.6,5-6.6,7-6.6,8-6.6,10-6.6\n\\end{Bmatrix}="

"=\\begin{Bmatrix}\n-3.6, - 1.6,0.4,1.4,3.4\n\\end{Bmatrix},"

"\\sigma^2=(-3.6)^2\\cdot \\cfrac{1}{5}+(-1.6)^2\\cdot \\cfrac{1}{5}+\\\\\n+0.4^2\\cdot \\cfrac{1}{5}+1.4^2\\cdot \\cfrac{1}{5}+3.4^2\\cdot \\cfrac{1}{5}=5.84."




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