What is the variance of {15, 9, -3, 8, 0}?

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What is the variance of {15, 9, -3, 8, 0}?

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Answer 1 · 2016-03-15T09:58:43

Variance $σ^{2} = \frac{1054}{25} = 42.16$ $sigma^2=1054/25=42.16$

Explanation:

We compute the arithmetic mean first

$μ = \frac{15 + 9 + (- 3) + 8 + 0}{5}$ $mu=(15+9+(-3)+8+0)/5$

$μ = \frac{29}{5}$ $mu=29/5$

To compute for variance $σ^{2}$ $sigma^2$ use the formula

$σ^{2} = \frac{\sum {(x - μ)}^{2}}{n}$ $sigma^2=(sum (x-mu)^2)/n$

$σ^{2} = \frac{{(15 - \frac{29}{5})}^{2} + {(9 - \frac{29}{5})}^{2} + {(- 3 - \frac{29}{5})}^{2} + {(8 - \frac{29}{5})}^{2} + {(0 - \frac{29}{5})}^{2}}{5}$ $sigma^2=((15-29/5)^2+(9-29/5)^2+(-3-29/5)^2+(8-29/5)^2+(0-29/5)^2)/5$

$σ^{2} = \frac{1054}{25} = 42.16$ $sigma^2=1054/25=42.16$

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What is the variance of {15, 9, -3, 8, 0}?

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