\documentclass{article}
\usepackage{german}
\begin{document}
Each of the measurements $x_1 < x_2 < \cdots < x_r$ occures
$p_1$-, $p_2$-$,\ldots,p_r$ times. The mean value and standard deviation
are then
\[ x = \frac{1}{n}\sum_{i=1}^r p_i x_i,\qquad s= \sqrt{\frac{1}{n}\sum_{i=1}^r
   p_i(x_i - x)^2} \]
where $ n = p_1 + p_2 +\cdots+p_r $.
\end{document}