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CDs as a rule are not compressed at all. They present the full Red book audio signal in non comprsssed format.
I am sure I added a lot of confusion, sorry about that . . ."
That is correct but it is confusing. The data on the CD is not compressed as such but many if not most CDs in the last 10 years or so are woefully compressed in terms of dynamic range.
Geoff is correct, the site he linked to is very helpful in terms of buying music and as mentioned the DR can vary widely between CD, LP and downloadable files of the same music released at the same time.
For a new audiophile one of the things that can tip you off in terms of dynamic range compression is the volume.
Put in Mark Knopfler's well produced Tracker CD. Set the volume at a moderate comfortable level. Listen to it. Then, pop it out and put in Alabama Shakes Boys and Girls CD. Do not change the volume....but hold your ears....the Alabama Shakes CD is horribly compressed and will be much louder. And even at a lower volume on your system it will make your ears tired. Subtlety is lost. And even a well written, well played album like Boys and Girls is ruined by terrible production.
And yes, as @wolf_garcia said, judicious use of compression is a necessity and nothing new in the recording world. Done properly it enhances the music. Done with a club and a hammer it ruins the music.