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interpolate

/ɪnˈtɜːrpəleɪt/·verb

to estimate a value between known points, or insert something into a text
Fig. 1 — Two readings sit on the graph paper — two o'clock and three, both measured, both solid — and the half-hour between them is blank.
01Definition

To interpolate is to put something in between — a value between two measurements, or a remark into someone else's text. In data work you interpolate when you estimate a point inside the range you have already measured: the gap is bridged from both sides. From Latin interpolare, 'to polish up, touch up', it kept a second life in scholarship, where an interpolation is a passage slipped into a manuscript by a later hand. Its mirror twin reaches the other way: to extrapolate is to leave the measured range entirely.

02In use
  • iFrom readings at 2:00 and 3:00 you can interpolate the half-past value with some confidence.
  • iiThe editor suspected a later scribe had interpolated the passage into the original text.
  • iiiMissing sensor values were interpolated so the model could infer a complete curve.
03Collocations
  • interpolate between known values
  • interpolate a value
  • interpolated from the data
  • interpolate a remark
  • linear interpolation

Family interpolation (noun) · interpolated (adjective) · interpolator (noun)

04Relations

=insert, interject, interpose, estimate, infer

≠extrapolate, excise

06TOEFL & IELTS

A precise STEM verb for TOEFL charts and data passages, and the in-range partner of extrapolate: you interpolate between measured points, extrapolate beyond them — an interpolated estimate is the safer of the two because both ends of it rest on data. Mind the stress: in-TER-puh-late, on the second syllable like interpret, not 'inter-POL-ate'. In academic prose the noun interpolation is actually the more frequent form, and the everyday collocation is 'interpolate between known values'.

07Asked
What does interpolate mean?
It has two live senses. In data and math, to interpolate is to estimate an unknown value that sits between values you have measured — as in the scene above, where the half-past temperature is read off a line drawn between the two known dots. In writing and speech, to interpolate is to insert something — a remark into a conversation, a passage into a text.
What is the difference between interpolate and extrapolate?
Both estimate unknowns from known data; the difference is where the unknown sits. Interpolating fills a gap inside the measured range, extrapolating projects beyond its edge — the prefixes carry the whole distinction, inter- 'between' versus extra- 'outside'. Remember it spatially: one bridges between known dots, the other leaps past the last of them.
What does interpolation mean in music?
In music, an interpolation is a melody or lyric from an earlier song re-recorded inside a new one — sung or played afresh rather than lifted from the original tape. That is what separates it from sampling, which reuses the actual recording: an interpolation needs only the composition's rights cleared; a sample needs the recording's rights too, which is usually costlier.
What does interpolate mean in math?
It means calculating an unknown value from the known data points around it. The simplest method is linear interpolation — assume a straight line between the two neighbours and read the value off it, as the scene above does for the 2:30 reading. Curved methods exist for wavier data, but the move is the one used whenever a table lists values for 10 and 20 and you need 15.
What is an interpolation in a text or manuscript?
A passage inserted into a text by someone other than its author — a scribe's addition, a later editor's 'improvement'. Textual scholars hunt interpolations when reconstructing what an original manuscript actually said, and several disputed verses in ancient works are argued to be exactly this. The word carries a quiet whiff of tampering in this sense: the insertion pretends to belong.
What is the noun form of interpolate?
Interpolation — and in academic prose it outnumbers the verb, naming both the act ('interpolation between data points') and the thing inserted ('a later interpolation in the manuscript'). A person or tool that interpolates is an interpolator, though that form is rare outside mathematics and engineering. The stress stays where the verb put it: in-ter-puh-LAY-shun expands from in-TER-puh-late.