The interquartile range, sometimes called the IQR, represents the range from the 25th percentile to the 75th percentile, or middle 50 percent of a data set. The interquartile range can be used to show what the range of an average performance would be, such as where most people fall on a certain test or what the average employee makes. The interquartile range can be more effective than the mean or median because it shows the dispersion range rather than just one number.

## Order Data Points

First, begin by ordering your data points from least to greatest. For example, if your data points were 10, 19, 8, 4, 9, 12, 15, 11 and 20, you would rearrange them like this: {4, 8, 9, 10, 11, 12, 15, 19, 20}.

## Determine First Quartile Position

Next, determine the position of the the first quartile using the following formula: (N+1)/4 where N is the number of points in the data set. If the first quartile falls between two numbers, take the average. In the above example, since there are nine data points, you would add 1 to 9 to get 10 and then divide by 4 to get 2.5. Since the first quartile falls between the second and third value, you would take the average of 8 and 9 to get 8.5.

## Determine Third Quartile Position

Determine the position of the the third quartile using the following formula: 3*(N+1)/4 where N is the number of points in the data set. If the third quartile falls between two numbers take the average. In the above example, since there are nine data points, you would add 1 to 9 to get 10, multiply by 3 to get 30 and then divide by 4 to get 7.5. Since the first quartile falls between the seventh and eighth value, you would take the average of 15 and 19 to get 17.

## Calculate Interquartile Range

Calculate the interquartile range by subtracting the value of the first quartile (step 2) from the value of the third quartile (step 3). Finishing the example, you would subtract 8.5 from 17 to find that the interquartile range equals 8.5.

## Advantages and Disadvantages of IQR

The interquartile range has an advantage of being able to identify and eliminate outliers on both ends of a data set. IQL also is a good measure of variation in cases of skewed data distribution. However, it has several disadvantages as compared to standard deviation: less sensitivity to a few extreme scores and a sampling stability that is not as strong as standard deviation.