By Kardi Teknomo, PhD .
Traditional variance formula is
We can rewrite the variance formula so that we can separate the term of mean from the summation
To simplify the notation, let us give symbol to the sum
Using this new symbol, we can write the variance as
Now we have corrected measurement data, which is to add with a new data and to minus with the wrong data . The corrected variance is
We can expand into
Then rearrange to get
And we simplify
See Also: proof of corrected mean formula
Preferable reference for this tutorial is
Teknomo, Kardi. (2006) Recursive Average and Variance.