Question

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

Answer 1

`"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`