*Interpolation* means to estimate something that lies between observations. For 
instance, if we have two snapshots of a bowling ball at different point in the 
lane, we can *interpolate* that it must have passed through the other points 
between those two points. Any kind of average is an interpolation, since we are 
making an estimate of the midpoint of the group by using the elements of the 
group that we can see.


*Extrapolation* means to extend a set of observations to some further point. 
For instance, if we have two snapshots of a bowling ball at different point in 
the lane, we can *extrapolate* whether it will hit the pins at the far end of 
the lane. We can also extrapolate backwards; in this case, we can extrapolate 
that someone rolled the bowling ball at a time before the first snapshot.


Interpolation and extrapolation both try to extend what we have observed—to 
what we have not observed, but do so in different directions or modes. 
Interpolation extends to what must have happened between observations, while 
extrapolation extends to what happens before, after, or beyond observations.


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