# Estimating a Population Stadev

Six Sigma – iSixSigma Forums Old Forums General Estimating a Population Stadev

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• #50526

gutierrez
Participant

Hi All – I was wondering if someone can help understand what is a population standard deviation.
There was a sevice guy who came in into our plant to work on gage he was using the following to calculate population standard deviation:
TO ESTIMATE POPULATION STANDARD DEVIATION DIVIDE AVERAGE RANGE BY 2.36
I copied this from his report. How did he come up with this number?
I though the formula was:

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#173765

Ron
Member

You haven’t got enough time to derive the equation..simply said the equation you wrote is for the population standrard deviation which we never know and is incorrect for an estimated SD.   hint (n-1)

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#173764

Robert Butler
Participant

You can compute an estimate of the standard deviation from estimates of the range.  It would appear that the rule your service guy was using was to compute an average range based on a sample of 5 ranges.  If you do this then the equation is
SD = Average Range/2.326
There isn’t a 2.36 – I suspect a miscopy.
pp. 139-141 Quality Control and Industrial Statistics 4th Edition – Duncan has the details.

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#173766

gutierrez
Participant

Thank you very much!!!

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#173793

David Klaus
Participant

I suggest you get the book “Gauge R&R Studies” by Mario Perez-Wilson.  It has all the formulas and how they are derived.
It’s the best source I have found.
D. Wheeler only treats the control chart method.
Douglas Montgomery’s book is too technical and not practical.
Gook luck

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#173796

Rothschild
Member

The “Overall” standard deviation is the square root of the sum of each observation minus the average square divided by the degrees of freedom (n-1).The “Within” standard deviation is a prediction of the sigma and is equal to the range average divided by d2.  d2 is a constant that depends on two factors.1. How many ranges were used to compute the average range.2. How many observations were used to compute each range.
What you refer to as the “overall” SD is used to calculate Ppk, and the “within” SD is used to calculate the Cpk.

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