Simple Interpolation and Extrapolation (IOD 404)

Interpolating means reading a value that falls inside the range of data already collected. If a table gives 20 C and 30 C, and the trend between them is smooth and close to a straight line, you can trust a number at 25 C because it sits boxed in by real measurements on both sides. The data itself is doing the checking: whatever the true shape of the curve is, it cannot do anything too wild in a gap that short without the two surrounding points catching it.

Extrapolating means stepping past the last point you actually measured. Nothing stops the real trend from curving, flattening, or reversing right after your data ends, so the farther out you reach, the less the fitted line or curve is actually describing. A trend line drawn through four points is only a summary of those four points. It makes no promise about a fifth point sitting outside that stretch, no matter how perfectly straight the fit looks.

Both skills sit next to reading trends and translating graphs into words: first you find the pattern, then you decide how far you are allowed to push it. A tight linear fit across a tested range is strong evidence inside that range and weak evidence anywhere past it, especially if the underlying process has a natural limit, like a reaction running out of reactant, which would flatten the real curve just beyond the data you have.