| Convert Raw Scores
to Cumulative Percentages
A raw score is a single score that is derived
from a test or an observation. Cumulative percentages determine
placement among a group of scores. Raw scores are also known
as X values and are usually not useful by themselves. Converting
raw scores into cumulative percentages allows for meaningful
comparisons.
For example, what if you received an 80 on an exam in your
biology class? (The 80 is a raw score.) If an 80 were the highest
grade in the class, your cumulative percentage would be 100%.
Since you scored at the 100th percentile, you did better than
or the same as everyone else in the class. That means that
everyone else made either an 80 or below on the exam. However,
what if your score of 80 corresponds to a cumulative percentage
of 40%? Then you did the same or better than 40% of the people
in your class. That means that 60% of the people in the class
made higher than an 80 on the exam.
In the above example, the same score was interpreted differently
in each situation. In the first example, an 80 could be seen
as a high grade. In the second example, an 80 could be seen
as a low grade. The interpretation of 80 depends on the other
scores in the class. Cumulative percentages are ranked on a
scale of 0-100. Changing raw scores to cumulative percentages
is one way to standardize raw scores within a certain population.
That’s why it is important to change raw scores into
cumulative percentages. The remainder of this handout explains
the general process and the specific steps to follow when you
convert raw scores to cumulative percentages.
**Note: Cumulative percentages do not determine how much greater
one score is than another or how much less it is than another.
Cumulative percentages are ranked on an ordinal scale and are
used to determine order [rank] only.
General Process
Choose the links below to learn more about each of the
stages in the process.
- List the categories of raw
scores (X scores—in this
case they are grades) in the first column.
- Determine
how many times each score occurs (the frequency) in the
second column.
- Determine how many scores are
at or below each score (cumulative frequency) in the third
column.
- Determine the percentage of
scores at or below each frequency (cumulative percentage)
in the last
column.
Also available . . .
suggested
resources.
Copyright 2005 by the Academic Center and the
University of Houston-Victoria.
Created 2004 by Maranda Koenig. Content Reviewed by Hari
Damodaran. Edited by Sandra Heinold. |
