The odometer is direct gear driven, the only thing that can
effect it's accuracy is a change in the rear gear ratio or
the tire diameter or a change in the driven gear at the transmission.
The needle on the other hand, is driven by a magnetic field
and can easily loose calibration from a dry bearing, a bad
bearing or damage to the air gap clearance if someone messed
with the head, the air gap sets the calibration.
A jerky needle is almost always caused by a worn or
sticking cable or cable housing.
dg
In your first post you posed this question, "how would you make the correction for a mpg calculation if your speedo read 5 mph slow??"
Based on your most recent post, is there still a valid reason for determining a correction based on 5 MPH speedometer reading (irrespective of the odometer)?
If so, then I would suggest that, while the math equation can be formulated, the premise of the request may be invalid. Is it off by 5 MPH at all speeds? If that is the case, your speedometer is defective. If the inaccuracy were due to gears/tire size, then the error would be a precise percentage of error at any given speed.
Carl