Index rebuild followed by statistics update

I inherited a SQL server with one maintenance plan which runs once per week and does these tasks in sequence:

Check Database Consistency

Rebuild Index

Update Statistics

Clean Up History

Maintenance Cleanup Task

I know this is a routine topic, but I need a refresher... isn't the Update Statistics task redundant to the Rebuild Index task?  Should Update Statistics task be broken out into its own job and run nightly, possibly along with a reorg index?

Thanks.