Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

SECTION 2.4 | Percentiles, Percentile Ranks, and Interpolation 53
Time
Pay
End
8 hours
$60
Known values
FIGURE 2.13
A visual representation
of the process
of interpolation. One
interval is shown on
two different scales,
time and pay. Only the
endpoints of the scales
are known. You start
at 0 for both time and
pay, and end at 8 hours
and $60. Interpolation
is used to estimate
values within the interval
by assuming that
fractional portions of
one scale correspond
to the same fractional
portions of the other
scale.
Start
6 hours
4 hours
2 hours
0 hours
3
4
1
2
1
4
$45
$30
$15
$0
Estimated values
Known values
b. Locate the position of the intermediate value in the interval. This position corresponds
to a fraction of the whole interval:
You may notice that in
each of these problems
we use interpolation
working from the top of
the interval. However,
this choice is arbitrary,
and you should realize
that interpolation can be
done just as easily working
from the bottom of
the interval.
fraction 5
distance from the top of the interval
interval width
c. Use the same fraction to determine the corresponding position on the other
scale. First, use the fraction to determine the distance from the top of the
interval:
distance = (fraction) × (width)
d. Use the distance from the top to determine the position on the other scale.
The following examples demonstrate the process of interpolation as it is applied to
percentiles and percentile ranks. The key to success in solving these problems is that
each cumulative percentage in the table is associated with the upper real limit of its score
interval.