What are the variance and standard deviation of {8, 29, 57, 3, 8, 95, 7, 37, 5, 8}?

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Answer 1 · 2016-01-21T21:33:35

$s=sigma^2=815.41->$ variance

$sigma=28.56->$ 1 standard deviation

The variance is a sort of mean measure of the variation of the data about the line of best fit.

It is derived from: $sigma^2=(sum (x-barx))/n$

Where $sum$ means add it all up

$barx$ is the mean value (sometimes they use $mu$ )

$n$ is the count of data used

$sigma^2$ is the variance (sometimes they use $s$ )

$sigma$ is one standard deviation

This equation, with a bit of manipulation end up as:

$sigma^2=(sum(x^2))/n - barx^2" "$ for variance

$sigma=sqrt((sum(x^2))/n - barx^2) " "$ for 1 standard deviation
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Rather than building a table of values I used a calculator to do the work for me:

$sigma^2=(sum(x^2))/n - barx^2" "$

becomes:

$sigma^2=14759/10-(25.7)^2$

$s=sigma^2=815.41->$ variance

$sigma=28.56->$ 1 standard deviation