The output will, by default, get sent to whichever user's crontab started the process. If this is the main crontab, then root gets the email.
If you want the mail sent somewhere else, you can either configure your MTA to forward the mail, or set
MAILTO from within the crontab to alter the destination. (Use
MAILTO="" to suppress mail entirely.)
if you install a cron and the cron job has an output >/dev/null, it will be sent to the system administrator
I believe you meant to say that the job does not have output redirected to
/dev/null; if all of the output is written to stdout, and stdout gets sent to
/dev/null, then there will be no output to send to anyone.