Range vs IQR
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Range
Describing data
The range is a measure of spread equal to the difference between the largest and smallest values in a data set.
The range measures spread as the distance between the two most extreme values. You compute it as . For example, if test scores run from 62 to 98, the range is points. Because it uses only the two extreme values, the range is highly sensitive to outliers and ignores everything in between.
Interquartile range (IQR)
Describing data
The interquartile range (IQR) is the spread of the middle half of the data, equal to the third quartile minus the first quartile.
The interquartile range measures how spread out the middle 50 percent of the data is, so it ignores the extreme quarters. You compute it as , the third quartile minus the first quartile. For example, if and , then the IQR is . Because it drops the top and bottom quarters, the IQR is resistant to outliers and drives the 1.5 times IQR rule for flagging them.