In the Monster Manual, the average hit points for each CR follows a clear pattern. This is an extra 15 hit points for each higher CR − until CR 22 when hit points leap off the rails. Then there is a sudden almost-100 extra hit points, and the hit points ramp up from there. It is like a car in traffic suddenly flying into the sky.
These wildly high hit points make one wonder if the hit points should be accelerating gradually all along, so the the entry into CR 22 is part of a smooth progression.
Defacto, the Damage Per Round accelerates at a smooth curve while advancing thru the CRs. One can expect the amount of damage that a monster can deal at a certain CR to correlate with how much damage the monster can withstand from others at that CR. Probably, the hit points should be accelerating at the same curve proportional to the DPR. The formula for the DPR curve involves the exponent CR^1.4. If this same exponent is used for a proportional formula for the hit points, the result is the "Curve" formula in the table below.
My feeling is the hit points generated at the mid upper CRs are a bit high. Even so, each CR includes some creatures that function as less powerful "mooks", and some creatures that function as very powerful "bosses". Part of the reason for the spike in hit points from CR 22 on up is, at those epic CRs, they are all bosses. So the higher hit points that the Curve formula generates are useful as a guideline for around where the hit points of bosses should be. Additionally, if a DM tends to find the creatures of a certain CR too easily focus-fired away, use the Curve as an approximate ceiling when deciding how many hit points to buff the creatures.
In the Hit Point table below, the actual average hit points in the 5.5 Monster Manual are in parentheses in the central column. The left column is the linear "Line" formula for hit points, that stays true until CR 22 when the hit points leap upward. In the right column, is the exponential "Curve" formula, that shows what a smooth acceleration of hit points looks like into the highest CRs. Significantly, this Hit Point Curve is proportional the DPR Curve for the damage dealing. For comparison, the numbers in red are lower than the MM average, being less than 90%, and the numbers in blue are higher than the MM average, being more than 110%.