**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**

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**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 Student Success Center and the University of Houston-Victoria.

Created 2004 by Maranda Koenig. Content Reviewed by Hari Damodaran. Edited by Sandra
Heinold.