A one pass calculation of standard deviation

Math Central

Quandaries & Queries

Hi
I searched the listings but couldn't find what i am looking for. I have a data set and i am allowed only 1 pass through it. At the end of this pass i must have the mean and standard deviation. Calculating the mean is easy as also demonstrated in your listings. I think the same can be done for standard deviation as well. But the doubt that i have is this :- Will the calculated standard deviation be sequence dependent ? i.e. if i change the order in which the data items enter the system, will the std deviation also change ??

Thanks in advance
Murtaza

Murtaza,

There are one pass expressions for the variance s² and then the standard deviation is the square root of the variance. One such expression is

If you can keep a running total of the data values x_i, the squares of the data values x_i² and the number of data values then you can assemble this expression after all the data is read once. This expression only uses the data values and the number of data values and not the order in which the values are read.

I hope this helps,
Penny

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