## interpolate and extrapolateTo interpolate is to estimate the value of a point that lies between
two known values of a function; this is
often done by approximating a line or a smooth
curve between the values, which is the literal
meaning of the word. Inter is the Latin prefix for "between," polire
translates as "to adorn or polish," so together they mean "to smooth between."
Extrapolate was created as an extension of interpolate
to suggest the smoothing of a line outside the known points. This
operation is often done in statistics when patterns are studied over time
to predict future events. Interpolation and extrapolation are techniques used in mathematical analysis to estimate undetermined values of a dependent variable, a number of values of which, corresponding to determined values of an independent variable, are known. This is done by finding a function f(x) of the independent
variable x such that, for any value, x, the
known corresponding value _{a}y of the dependent variable
_{a}y closely approximates to the value f(x.
In interpolation it is then assumed that, within the range covered by the
known values of the variables, _{a})y = f(x) for all intermediate values
of x and y. In extrapolation, one assumes this relationship
to hold outside the range of known values – a rather less justifiable
assumption. The simplest (and most commonly used) technique is that of drawing
the best straight line or curve through a set of points on a graph, and
assuming that it represents a genuine relationship between the two variables
in question. Others include the use of partial difference
equations. ## Related category• APPROXIMATIONS AND AVERAGES | |||||

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