Upgrade from 8.4 to 9.4.1

I am using a Mac with the latest operating system Yosemite.

The upgrade instructions I have found in the archive confuse me in one way:

I would like to upgrade to Postgres.App. In their instructions they say,

"For best results, you should remove any existing installation of
PostgreSQL. Here's a run-down of the most common ways you may have
installed it previously:"

However, in the instructions on this list, it is recommended (strongly) to
use the pg_dump contained in the version you wish to upgrade to to transfer
your tables.

I do not understand how I can remove the existing installation with the
mission-critical data it contains and use pg_dump from the new version to
access that data.

I know I am missing something. Please tell me what.

Thank you very much,

John Gage