Interpolate first in the x-direction and then in the y-direction or vice-versa and
show that
Fα=(1 −α)F 11 +αF 12 , F β= (1 −β)F 11 +βF 21
Fα,β =(1 −α)(1 −β)F 11 +α(1 −β)F 12 +β(1 −α)F 21 +αβF 22
Note how the Fα and Fβ values vary as the
parameters αand β vary from 0 to 1. This is a
straight forward linear interpolation between the
given values. The value Fα,β is obtained by first
doing a linear interpolation in the y direction at
the columns x 1 and x 2 , which is then followed by
a linear interpolation in the x-direction.
An alternative method of interpolation is to
use the Taylor series expansion in both the xand y
directions to obtain the alternative interpolation
formula
Fα,β = (1 −α−β)F 11 +βF 21 +αF 12
Sometimes it is necessary to modify the above interpolation formulas for appli-
cation to entries in a three-dimensional array of numbers. The interpolation result
is obtained by applying the one-dimensional interpolation formulas in each of the
x, y and zdirections.
Statistical Tables
This introduction to the study of statistics concludes with some well known
statistical tables. These tables are employed in various types of statistics testing.
Statistical tables in many forms where extensively used prior to the advent of com-
puters. The internet provides the access to a much larger variety of statistical tables.
