If you only have directories and not files in directory1, then the following two "commands" should give you the size (in bytes) and name of the largest directory and the average of their sizes (in bytes), respectively.
$ du -sb directory1/* | sort -n | tail -n 1
$ du -sb directory1/* | awk ' { sum+=$1; ++n } END { print sum/n } '
If there is also ordinary files within directory1, these will be counted as well with the examples above. If ordinary files should not be counted, the following might be more appropriate.
$ find directory1/ -mindepth 1 -maxdepth 1 -type d -exec du -sb {} \; | sort -n | tail -n 1
$ find directory1/ -mindepth 1 -maxdepth 1 -type d -exec du -sb {} \; | awk ' { sum+=$1; ++n } END { print sum/n } '