A large portion of western media is state-funded public broadcasters (the BBC, CBC, PBS, ...), and another large swathe is under the control of various explicitly right-leaning corporations (Murdoch's News Corp and Fox, Sinclair, ...).
While there are indeed numerous liberal-leaning media outlets, it is entirely unclear to me that they have equivalent reach to their conservative counterparts.
If you consider PBS and BBC to somehow be conservative I guess that's why things are entirely unclear to you. What on earth would you like me to cite?
plurality /ploo͝-răl′ĭ-tē/
noun
A large number or amount; a multitude.
Ahem..
If you consider NPR to be far-far left then what is Jezebel, The Young Turks, Jacobin, or Democracy Now? That's not even getting into things like Socialist Alternative or pod casts like Chapo Trap House.
Between the ones I listed and NPR are sites like Slate and Vox which are to the left of NPR but not as far left as Democracy Now.
Probably not by number of outlets, either, not that it would matter.
The dominant Western media position is center-right neoliberal corporate capitalist (unsurprisingly, reflect both the ruling class of Western society and, as its the same class, the class that predominantly owns corporations, including media corps.)