By Kardi Teknomo, PhD .

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Traditional variance formula is Corrected Variance
We can rewrite the variance formula so that we can separate the term of mean from the summation
Corrected Variance
To simplify the notation, let us give symbol to the sum
Corrected Variance
Corrected Variance
Using this new symbol, we can write the variance as

Corrected Variance
Now we have corrected measurement data, which is to add with a new data Corrected Variance and to minus with the wrong data Corrected Variance . The corrected variance is
Corrected Variance
We can expand into
Corrected Variance
Corrected Variance
Then rearrange to get

Corrected Variance
And we simplify

Corrected Variance
Corrected Variance (proved)


See Also: proof of corrected mean formula

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These tutorial is copyrighted .

Preferable reference for this tutorial is

Teknomo, Kardi. (2006) Recursive Average and Variance.
http://people.revoledu.com/kardi/tutorial/RecursiveStatistic/index.html