So what it comes to is that everything at CR 1 generally causes similar levels of grief for the party, but they may go about it differently. Average is.625, and it was rounded up to 1. Average DPR of 13.33 starts OCR at 1 and AB of +4 leaves that unchanged. The Bugbear: HP 27 starts at DCR 1/8, AC 16 brings that up to DCR 1/4. DPR 19 starts OCR at 2, AB of +5 brings that to OCR of 3. The Brown Bear: HP 34 starts at DCR 1/8, AC 11 brings that to DCR 0.
Other traits will affect the effective HP, AC, DPR, and AB as well. CR is also the average of the defensive and offensive CRs. This does not necessarily line up with what is printed in a stat block. The suggested values are for 'effective' HP, AC, DPR, and AB.