[Numpy-discussion] non-standard standard deviation

Colin J. Williams cjw@ncf...
Sat Dec 5 13:28:12 CST 2009

On 04-Dec-09 07:18 AM, yogesh karpate wrote:
> @ Pauli and @ Colin:
>                                   Sorry for the late reply. I was busy 
> in some other assignments.
> # As far as  normalization by(n) is concerned then its common 
> assumption that the population is normally distributed and population 
> size is fairly large enough to fit the normal distribution. But this 
> standard deviation, when applied to a small population, tends to be 
> too low therefore it is called  as biased.
> # The correction known as bessel correction is there for small sample 
> size std. deviation. i.e. normalization by (n-1).
> # In "electrical-and-electronic-measurements-and-instrumentation" by 
> A.K. Sawhney . In 1st chapter of the book "Fundamentals of 
> Meausrements " . Its shown that for N=16 the std. deviation 
> normalization was (n-1)=15
> # While I was learning statistics in my course Instructor would advise 
> to take n=20 for normalization by (n-1)
> # Probability and statistics by Schuam Series  is good reading.
> Regards
> ~ymk

Thanks for the Bessel name, I hadn't come across that before.

The Wikipedia reference for the Bessel Correction uses a divisor of n-1: 

Perhaps the simplification for larger n comes from the fact that for 
large n, 1/n  => 1/(n-1).

I would suggest C. E. Weatherburn - Mathematical Statistics,  but I 
doubt whether it is still widely available.

Colin W.

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