Weighted Standard deviation

Posted on 2013-09-12
Medium Priority
Last Modified: 2013-09-12
I found the attached 'weightsd.pdf' formula for weighted standard deviation from NIST.

Wolfram  shows the variance of the weighted mean in equation 24 in the 'maximum likelihood' attachment.  

The link to Wikipedia below states the same formula in hte Wolfram article for determining the weighted standard deviation on the link below:


My question is, I have yet to be able to reconcile the formula in the NIST attachment with the Wolfram and Wikipedia results, and was wondering which was the more apropriate approach to use (NIST or Wolfram) and why.

Thank you
Question by:aasikolo
  • 2
  • 2
LVL 27

Accepted Solution

aburr earned 1000 total points
ID: 39488597
I do not blame you for being confused. The notation and sentence construction in wiki is difficult.
Not that the capital values (X and Xbar) are already weighted while the x and xi in the NIST equation are not.

Author Comment

ID: 39488964
What is xbar sub w if it is not weighted in the NIST equation?  I see the xi but no x in the NIST equation.  Did you mean x bar sub w and xi are not weighted in the NIST equation?

To confirm, If I manage to decipher this mess, both formulas should yield the same result?

Thank you

Author Closing Comment

ID: 39488984
Examples with calculations help.  I'll send calculations when they aren't proprietary.
LVL 27

Expert Comment

ID: 39489068
"Did you mean x bar sub w and xi are not weighted in the NIST equation?"
the xi are not weighted but the x (or as I should have said) x bar sub w is.
Use the nist. It is clearer.

Featured Post

Free Tool: ZipGrep

ZipGrep is a utility that can list and search zip (.war, .ear, .jar, etc) archives for text patterns, without the need to extract the archive's contents.

One of a set of tools we're offering as a way to say thank you for being a part of the community.

Question has a verified solution.

Are you are experiencing a similar issue? Get a personalized answer when you ask a related question.

Have a better answer? Share it in a comment.

Join & Write a Comment

Article by: Nicole
This is a research brief on the potential colonization of humans on Mars.
When we purchase storage, we typically are advertised storage of 500GB, 1TB, 2TB and so on. However, when you actually install it into your computer, your 500GB HDD will actually show up as 465GB. Why? It has to do with the way people and computers…
This is a video describing the growing solar energy use in Utah. This is a topic that greatly interests me and so I decided to produce a video about it.
I've attached the XLSM Excel spreadsheet I used in the video and also text files containing the macros used below. https://filedb.experts-exchange.com/incoming/2017/03_w12/1151775/Permutations.txt https://filedb.experts-exchange.com/incoming/201…

621 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question