What is the variance of the following numbers?: {2,9,3,2,7,7,12}

1 Answer
Apr 10, 2016

#"Variance"_"pop." ~~ 12.57#

Explanation:

Given the terms: #{2,9,3,2,7,7,12}#

Sum of terms: #2+9+3+2+7+7+12=42#
Number of terms: #7#
Mean: #42/7=6#

Deviations from Mean: #{abs(2-6), abs(9-6),abs(3-6),abs(2-6),abs(7-6),abs(7-6),abs(12-6)}#

Squares of Deviations from Mean: #{(2-6)^2, (9-6)^2,(3-6)^2,(2-6^2),(7-6)^2,(7-6)^2,(12-6)^2}#

Sum of Squares of Deviations form Mean: #(2-6)^2,+(9-6)^2+(3-6)^2+(2-6^2)+(7-6)^2+(7-6)^2+(12-6)^2=88#

Population Variance #= ("Sum of Squares of Deviations from Mean")/("Count of Terms") = 88/7 ~~12.57#