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Bessel's Correction

The factor $(N-1)/N$ in the relationship between the Variance $\sigma$ and the Expectation Values of the Sample Variance,

\begin{displaymath}
\left\langle{s^2}\right\rangle{}={N-1\over N}\sigma^2,
\end{displaymath} (1)

where
\begin{displaymath}
s^2\equiv \left\langle{x^2}\right\rangle{}-\left\langle{x}\right\rangle{}^2.
\end{displaymath} (2)

For two samples,
\begin{displaymath}
\hat \sigma^2 = {N_1{s_1}^2+N_2{s_2}^2\over N_1+N_2-2}.
\end{displaymath} (3)

See also Sample Variance, Variance




© 1996-9 Eric W. Weisstein
1999-05-26