If a researcher observes that 32 out of 40 scores in a dataset are lower than a participant's score of 23, what is the percentile rank of the score of 23?

To find the percentile rank of a specific score, count the number of scores in the distribution that are lower than it, and convert that number to a percentage of the total number of scores. For example, if $$32$$ out of $$40$$ scores (which is $$80\%$$) are lower than a score of $$23$$, then the score of $$23$$ has a percentile rank of $$80$$.

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The percentile rank of an individual score describes its relative location within a distribution. It is defined as the percentage of all scores in the distribution that are strictly lower than that specific score. This measure provides a standardized way to compare an individual's performance against the rest of the group and is frequently used to report results on standardized tests of ability or achievement.

Percentile Rank

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KPU Research Methods in Psychology - 4th American Edition

To calculate a percentile rank, one counts the number of scores in a distribution that fall below a specific value and converts that count into a percentage of the total number of scores. For example, in a distribution of $$40$$ self-esteem scores, if $$32$$ of the scores are strictly lower than $$23$$, the percentile rank for a score of $$23$$ is calculated as $$(32 / 40) 	imes 100 = 80\%$$. Therefore, a student with a score of $$23$$ has a percentile rank of $$80$$, meaning they scored higher than $$80\%$$ of the individuals who took the test.

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