Percentiles are used to determine where a score fits in among all of the scores. For example, a score of 140 on a test does not mean anything unless you know how other people scored. If 90 percent of the people scored lower than a 140, the score is excellent. However, if only 10 percent of people scored lower than 140, the score is not so good. Percentiles are used to represent the percentage of scores lower than a given score.
Step 1
Divide the percentile that you are looking for by 100. For example, if you are finding the 40th percentile, you would divide 40 by 100 to get 0.4.
Step 2
Add 1 to the number of values in your data set. For example, if you had 30 test scores, you would add 1 to 30 to get 31.
Step 3
Multiply the value from Step 1 by the value from Step 2. If the result is a whole number, the Nth lowest score would be that percentile, where N is the whole number. For example, if the result was 4, the fourth lowest score. If the number is not a whole number, continue to Step 4. In this example, you would multiply 0.4 by 31 to get 12.4, which is not a whole number, so you would continue to Step 4.
Step 4
Split the result from Step 3 into the integer component, I, and the decimal component, D. In this example, you would split 12.4 into 12 for the integer component and 0.4 for the decimal component.
Step 5
Add 1 to the integer component. In this example, you would add 1 to 12 to get 13.
Step 6
Find the raw data scores for the integer component and the integer component plus 1. In this case, you would be looking for the 12th and 13th lowest scores, which for this example will be 75 and 78.
Step 7
Calculate the difference in the two scores from Step 6. In this example, you would subtract 75 from 78 to find the difference of 3.
Step 8
Multiply the difference from step 7 by the decimal component from Step 3. In this example, you would multiply 3 by 0.4 to get 1.2.
Step 9
Add the result from Step 8 to the value of the integer component's raw value. In this case, the integer component is 12 and the 12th lowest score was 75, so you would add 1.2 to 75 to find that the 40th percentile would be 76.2.