An Alternative Definition for IQR. In some texts, the interquartile range is defined differently. It is defined as the difference between the largest and smallest values in the middle 50% of a set of data. To compute an interquartile range using this definition, first remove observations from the lower quartile.Then, remove observations from the upper quartile. Then, from the remaining observations, compute the difference between the largest and smallest values.t is defined as the difference between the largest and smallest values in the middle 50% of a set of data. To compute an interquartile range using this definition, first remove observations from the lower quartile. Then, remove observations from the upper quartile.