INTERPOLATION AND EXTRAPOLATION
This chapter covers the use
of interpolation and extrapolation to solve for unknowns on various types of
graphs.
EO1.17 Given
a graph, SOLVE for the unknown using extrapolation.
EO1.18 Given
a graph, SOLVE for the unknown using interpolation.
Definitions
Interpolation Interpolation is the process of obtaining a
value from a graph or table that is located between major points given, or
between data points plotted. A ratio process is usually used to obtain the
value.
Extrapolation Extrapolation is the process of obtaining a
value from a chart or graph that extends beyond the given data. The
"trend" of the data is extended past the last point given and an
estimate made of the value.
Interpolation
and Extrapolation
Developing a curve from a set of data provides the student
with the opportunity to interpolate between given data points. Using the curve
in the following example, the value of the dependent variable at 4.5 can be
estimated by interpolating on the curve between the two data points given,
resulting in the value of 32. Note that the interpolation is the process of
obtaining a value on the plotted graph that lies between two given data points.
Extrapolation is the process in which information is gained from plotted data
by extending the data curve beyond the points of given data (using the basic
shape of the curve as a guide), and then estimating the value of a given point
by using the extended (extrapolated) curve as the source. The above principles
are illustrated in the example that follows.
Example:
Given
equation y = x^{2} + 2x + 3:
Plot
the curve for x from 0 to 5.
Extrapolate
the curve and give the value of y at x = 6.
Put
6 into the equation evaluating y, then compare the values.
Interpolate
the curve at x = 4.5.
Put
4.5 into the equation evaluating y, then compare the values.
Extrapolating
x = 6 gives a value of y = 48. Using the equation, the actual value of y is 51.
Interpolating x = 4.5 gives a value of y = 32. Using the equation, the actual
value of y is 32.25.
Summary
The
important information in this chapter is summarized below.
Interpolation
and Extrapolation Summary
Interpolation Interpolation is the process of obtaining a
value from a graph or table that is located between major points given, or
between data points plotted. A ratio process is usually used to obtain the
value.
Extrapolation
Extrapolation is the process of obtaining a value from a chart or graph that
extends beyond the given data. The "trend" of the data is extended
past the last point given and an estimate made of the value.
