You'll want to look at the average to get the rms over the whole track.
However, one should always avoid compressing/processing by the numbers. Use your ears, not your eyes. Wether something 'needs' compression is entirely down to what you want the end result to sound like - there is more than one way to approach dynamics processing and going by the numbers will not get you there by the quickest route.
Get a compressor, experriment with it, see what it does, and then decide if you want to use it.
The numbers can be a bit of a red herring and catch quite a few people out.
a little confusing...the diff between your peak values and your rms values helps you determine your crest factor,
which is more important when mastering,
not so much with mixing.
you do not have much dynamic range NOW...... with those numbers...
why would you want to diminish it even more with compression?
Of the two peak numbers the smaller one indicates your absolute headroom. In your example, if you boost the level more than 4.88dB the right channel will clip.
Of the RMS numbers the Average is the one that represents the whole song. The other two numbers are for some unspecified smaller time period, to give you an idea of level variations in your mix.
so peak = -5.48 and RMS = -16 ????
and does this track need compressing???