What is the variance of {15, 14, 13, 13, 12, 10, 7}?

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What is the variance of {15, 14, 13, 13, 12, 10, 7}?

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Answer 1 · 2015-11-01T04:08:07

Variance of the data set is $6.29$ $6.29$ .

Explanation:

Note that the formula of variance for calculation purpose is

$\frac{1}{n} n \sum i = 1 x_{i}^{2} - {(\frac{1}{n} n \sum i = 1 x_{i})}_{i}^{2}$ $1/n sum_(i=1) ^n x_i^2 - (1/n sum_(i=1)^n x_i)^2$

where $n$ $n$ is the total number of values in the given data set.
In your given data we have $n = 7$ $n = 7$ and the values of $x_{i}$ $x_i$ 's are ${15, 14, 13, 13, 12, 10, 7}$ ${15, 14, 13, 13, 12, 10, 7}$ .

So, your variance $= \frac{1}{7} [15^{2} + 14^{2} + 13^{2} + 13^{2} + 12^{2} + 10^{2} + 7^{2}] - {(\frac{1}{7} \cdot [15 + 14 + 13 + 13 + 12 + 10 + 7])}^{2}$ $= 1/7 [ 15^2+14^2+ 13^2 +13^2+12^2+10^2+7^2 ] - (1/7 *[ 15+14+13+13+12 +10 +7])^2$
$= 150.29 - 144$ $= 150. 29 -144$
$= 6.29$ $=6.29$

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What is the variance of {15, 14, 13, 13, 12, 10, 7}?

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