Arrange the numbers of a set in order from least to greatest. For example, you might have {5, 20, 6, 5, 7, 8, 15}. You would arrange these numbers as follows: 5, 5, 6, 7, 8, 15, 20.
Count the number of values in the set. Add 1 to the total and divide by 2 to find the median. In this example, you have 7 values. Add 1 to get 8 and divide by 2 to get 4. Therefore, the fourth value is the median, which corresponds to the number 7 in this example.
Look for the number that occurs most often. This is the mode. In this example, the number 5 occurs twice, which makes it the mode.
Determine the lower quartile value. This is the median for the lower half of the set of data. Add 1 to the number of values in the set. In this case, you have 7 values, plus 1 equals 8. Divide your answer by 4, which will give you 2 in this example. This means that the value in the second place within the set is the lower quartile, which in this case is 5.
Find the upper quartile value, which is the median for the higher half of values in the set. Add 1 to the number of values to get 8 in this example. Multiply your answer times 3 and then divide by 4. In this case, 8 times 3 is 24, and 24 divided by 4 is 6. Therefore, the sixth value in this set is the upper quartile. This corresponds with the value 15.
Calculate your interquartile range by subtracting the lower quartile from the upper quartile. In this example, you would subtract 5 from 15 to get 10.
Multiply your answer from Step 3 by 1.5. In this example, 10 times 1.5 is 15. Subtract this from the lower quartile to find the limit for any mild outliers. In this case, you would subtract 15 from 5 to get -10. Any value less than -10 would be a mild outlier. Add 15 to the upper quartile to find any upper level mild outliers. When you add 15 to 15, you get 30. Any number above 30 would be a mild outlier.
Multiply the interquartile range times 3. In this case, you would multiply 3 times 10 to get 30. Subtract this from the lower quartile to find extreme lower outliers. In this example, you would subtract 30 from 5 to get -25. Any value below -25 would be an extreme outlier. Add 30 to the upper quartile to get 45. Any value above 45 in this case, would be an extreme outlier as well.