Question

How is the rangeof a set of data different from a IQR

Answer 1

Suppose you're given a set of data.  Arrange it in ascending order, from smallest to largest.  

The "range" of this data can be thought of as "smallest to largest."  Alternatively, you could subtract the smallest value from the largest and call that the "range" of the data set.  That's it.

On the other hand, finding the IQR of a data set requires more work.  Again, arrange the data in ascending order.  Now identify the median as well as the first and third quartiles.  Subtract the first quartile from the third quartile.  The result is your IQR.

The tradeoff in doing more work to find the IQR is that the results tell us more about how the data set is distributed.

Answer 2

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.