What is the relationship between variance and standard deviation?

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What is the relationship between variance and standard deviation?

Mathematics
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Standard deviation = sqrt(variance), variance = standard deviation^2
that's all? okay!
yes

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oh cool. i was expecting something long and complicated, like what they actually do, what their purpose is
Well, say you have a data set, say, {1,2,3,4,5,6}.. the standard deviation of this data set would simply be the square root of the sum of the differences between each element and the average squared, divided by the number of elements....
Well, say you have a data set, say, {1,2,3,4,5,6}.. the standard deviation of this data set would simply be the square root of the sum of the differences between each element and the average squared, divided by the number of elements....\[\sigma = \sqrt{((x _{1}-x)^2+(x _{2}-x)^2...+(x _{k}-x)^2)/k}\]
x being the average, k being the number of elements in the data set, and that funny looking symbol (sigma) signifying standard deviation. k divides the sum of all of those numbers, just in case it isn't clear.
yh sure

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