What is the variance of {5, 3, 6, 14, 8, 10, 3, 17, 19, 9}?

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Answer 1 · 2016-04-05T03:57:28

$σ^{2} = 28.64$ $sigma^2 = 28.64$

There are 10 numbers, so $N = 10$ $N = 10$ .

First find the mean

$μ = \frac{\sum X}{N}$ $mu = (sumX)/N$

$= 9.4$ $= 9.4$

The variance is calculated as follows

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

$= 28.64$ $= 28.64$

Alternatively, use the equivalent formula

$σ^{2} = \frac{1}{N} (\sum X^{2} - \frac{{(\sum X)}^{2}}{N})$ $sigma^2 = 1/N ( sumX^2 - (sumX)^2/N )$

$= 28.64$ $= 28.64$