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