The variance of the sample consisting of the values 2,4,6,8,10 is
A) 6
B) 8
C) 10
D) 12

Question

Quizplus · Accepted Answer

The variance is the sum of squared deviations divided by the degrees of freedom. $$s ^ { 2 } = \frac { S S } { d f }$$ This can be calculated with the deviations from the mean (of 6)and the df = n-1: [(2-6)² + (4-6)² + (6-6)² + (10-6)²] / (5-1)= (16 + 4 + 0 + 16)/4 = 10 Or one could use the computational formula of $s ^ { 2 } - \frac { \sum _ { i = 1 } ^ { n } X _ { i } ^ { 2 } - \left[ \left( \sum _ { i = 1 } ^ { n } X _ { i } \right) ^ { 2 } / n \right] } { n - 1 }$ =[(4+16+36+64+100)- (30)²/n] / (n-1)= (220-180)/4 = 40/4 = 10

The Variance of the Sample Consisting of the Values 2,4,6,8,10