

\subsection{\bf Robust Determination of Mean}
\subsection{\bf Trimmed Mean}

\begin{slide}
\begin{itemize}
\item One method that is more robust than the arithmetic
mean, is the trimmed mean
\[
\mu^*_{\,\rm trim} = \frac{{\displaystyle\sum^{N(1-p)}_{i=pN+1}} 
x^{(i)}}{N(1-2p)}
\]
where $pN$ events are left off each end.  

\item For the special case of distributions symmetric about their mean,
the trimmed $\mu^*$ will also have mean $\mu$ and error $\alpha
\frac{1}{\sqrt{N}}$.

\item The variance of $\mu^*_{\,\rm trim}$ will be larger than
$\mu^*_{Am}$ for Gaussianly distributed $x^{(i)}$.

\item But as you investigate distributions broader than Gaussians you
will find the variance of $\mu^*_{\,\rm trim}$ becoming smaller than
that of $\mu^*_{Am}$.

\item A special case of $\mu^*_{\,\rm trim}$ is the median (i.e.,
middle value of $x^{(i)}$ when they are numerically ordered) gotten
with $p=0.5$.
\end{itemize}
\end{slide}

