# Pooled Standard Deviation

Six Sigma – iSixSigma Forums Old Forums General Pooled Standard Deviation

Viewing 7 posts - 1 through 7 (of 7 total)
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• #47575

Kiran Varri
Participant

Hi Guys,
Can some one offer an example for calculating Pooled Standard Deviation.
Thank you.
Kiran Varri

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#158814

David O’ C
Participant

COuld someone show the pooled Standard Deviation for this set of data,56.5256.5356.5856.5356.5356.5756.5556.5556.5856.5756.5756.55Thanks, David.

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#158815

Craig
Participant

You have not given enough information. If the data falls into one group, there is no need to pool the standard deviation.

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#158817

Snow
Participant

HACL,
Can you simply take the average of your subgroup std dev or is it necessary to break it down accordingly into SOS and DOF componennts as shown in the Dictionary definition on this site?

THANKS

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#158819

Craig
Participant

Don’t average, but pool as follows:

s2p = [(n1  1) s12  + (n2  1) s22] / (n1 + n2 -2)

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#159235

May
Participant

do you know any online programs that will calculate the pooled standard deviation? ive been searching for one but cant find it.

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#159247

Jim Ace
Participant

May, your question is a good one!  The pooled standard deviation can be estimated by the equation:
Spooled = sqrt[SSwithin / g(n-1)]
Notice that Spooled assumes your data is organized into groups (g = the number of groups and n = the number of replicates within each group).  Also notice that this equation requires the same sample size for each group.  You can also estimate the pooled standard deviation using Rbar/d2.  There are several other minor theoretical considerations that can be argued, but overall, you are safe with this method of analysis.
Extra Insight: See ANOVA    SStotal = SSwithin + SSbetween
For a more complete understanding of the pooled standard deviation you should look at the Minitab help menu.  Several of the computational methods in Minitab relies on the pooled standard deviation and gives you some good options on how it can be computed, like when you are attempting to estimate process capability.
Jim Ace

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