  Consider partitions of an open, bounded domain in $\mathbb{R}^n$. Then an
average element of the partition has either its Fraenkel asymmetry or its
deviation from the smallest element in the partition bounded away from 0 by a
universal constant. As an application, we give an (unspecified) improvement of
Pleijel's estimate on the number of nodal domains of a Laplacian eigenfunction
similar to recent work of Bourgain and improve a bound coming from spectral
partition problems.
