How can estimates of the mean and standard deviation of a series of observations be updated in a...

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Problem

How can estimates of the mean and standard deviation of a series of
observations be updated in a numerically stable way as each new
observation arrives?

[ Editor: problem statement reconstructed from the postings.  The
  original question (filed under the name "cars") was not preserved;
  only the reply giving a reference survives. ]

Show solution

No solution was found in the collected postings.  The one surviving
reply gives a reference:

See Lloyd S. Nelson, "Further Remark on Stably Updating Mean and
Standard Deviation Estimates," CACM, Vol. 22 (8), August, 1979, p. 483.
He also gives three references.

-- Peter Montgomery