The
Percentile Rank of a score is the percentage of individuals with scores
at or below the particular value. This
is equivalent to the cumulative relative frequency number, multiplied by 100.
A Percentile
is the score identified by the given percentile rank.
Many
values may not appear directly in a frequency distribution table, especially if
we are using class intervals rather than individual scores.
Suppose
we want to determine the percentile rank for such a score. Or the percentile for
a given percentile rank.
It
is possible to obtain estimates by using a process called interpolation.
This
process allows us to estimate intermediate values, if we assume that the change
from one end of the scale to the other is a regular, linear change.
1.
A single
interval is measured on two separate scales. The endpoints of the interval are known for each scale.
2.
You have
an intermediate value on one of the scales, and need to find the corresponding
intermediate value on the other.
1.
Find the
width of the interval on both scales.
2.
Locate
the position of the intermediate value in the interval (it will be a fraction of
the interval)
Fraction = distance from the top of the interval/
interval width
3. Use the fraction to
determine the distance from the top of the interval on the other scale.
Distance = fraction x width
4.
Use the distance from the top to determine the position on the other scale.