What is the variance of {51, 3, 9, 15, 3, -9, 20, -1, 5, 3, 2}?

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What is the variance of {51, 3, 9, 15, 3, -9, 20, -1, 5, 3, 2}?

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Answer 1 · 2016-03-12T13:10:20

Variance $σ^{2} = \frac{27694}{121} = 228.876$ $" " "sigma^2=27694/121=228.876$

Explanation:

Compute the mean $¯ x$ $barx$ first

$¯ x = \frac{51 + 3 + 9 + 15 + 3 + (- 9) + 20 + (- 1) + 5 + 3 + 2}{11} = \frac{101}{11}$ $barx=(51+3+9+15+3+(-9)+20+(-1)+5+3+2)/11=101/11$

Variance $σ^{2} = \frac{\sum {(x - ¯ x)}^{2}}{n}$ $" " "sigma^2=(sum(x-barx)^2)/n$

$σ^{2}$ $" " "sigma^2$
$=((51-101/11)^2+(3-101/11)^2+(9-101/11)^2+(15-101/11)^2+ (3-101/11)^2+(-9-101/11)^2+(20-101/11)^2+(-1-101/11)^2+(5-101/11)^2+ (3-101/11)^2+(2-101/11)^2)/11$

$" " "sigma^2=27694/121=228.876$

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What is the variance of {51, 3, 9, 15, 3, -9, 20, -1, 5, 3, 2}?

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