John Randall wrote:
The denominator of the sample mean really should be n, and for the
sample variance it really should be n-1 if you are estimating the
population mean from the sample.
"Should" is such a strong word, i do not think it is justified here.
Besides you dropped the disclaimer "if you want unbiased estimation of
population variance"
What i mean is that unbiasedness is not sacred. For example assiming normal
xi,
E((1/n-1)\sum (X_i-\bar X)^2 gives unbiased estimate, but E(1/n\sum
(X_i-\bar X)^2 gives another estimate, which though is biased, nevertheless
is optimal in least square sense. I am not saying that least square criteria
is more sacred than unbiasedness, but nor is other way around.
Bottomline is: one cannot just plug numbers into formula, one must know what
she is doing.
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