You don't. At least not for an install these days. Their data point must have been from a few years earlier.

My experience having installed one a couple of months ago is that the installer charged around 1.5k AUD just for the installation(by my calculation using retail prices) for a back to back "simple" install for the same brand and size mentioned. This is in Melbourne, Australia.

I did get multiple quotes that were the same and this was before peak summer season. The ones that were lower were either not licensed or wanted to do it for cash - meaning they wouldn't declare and pay taxes on it so the customer gets it for cheaper. It also means they won't give you an invoice and good luck claiming damages without evidence.

They blame the high cost of living but knowing some insiders, the margins are huge.

It's a pretty big market here I guess - this is for a simple installation, of course, with the mini split on a wall back to back with the external wall, running the piping down and hooking up and gassing. But that's about the standard price everyone was charging for that when I put my last one in two years ago. If you were putting in a ducted system obviously it would cost more.