Converting to Percentiles and Back (1 of 4)

If the mean and standard deviation of a normal distribution are known, it is relatively easy to figure out the percentile rank of a person obtaining a specific score. To be more concrete, assume a test in Introductory Psychology is normally distributed with a mean of 80 and a standard deviation of 5. What is the percentile rank of a person who received a score of 70 on the test?

Mathematical statisticians have developed ways of determining the proportion of a distribution that is below a given number of standard deviations from the mean. They have shown that only 2.3% of the population will be less than or equal to a score two standard deviations below the mean. (click here to see why 70 is two standard deviations below the mean.) In terms of the Introductory Psychology test example, this means that a person scoring 70 would be in the 2.3rd percentile.

normal distributiion

This graph shows the distribution of scores on the test. The shaded area is 2.3% of the total area. The proportion of the area below 70 is equal to the proportion of the scores below 70.