1.7 Range
Definition 1.28. The range is the difference between the largest and smallest observations: \[\text {Range}=X_{\max }-X_{\min }.\]
It is the quickest measure of spread to compute, and the least informative. It uses only two of the observations and ignores everything between them, so it says nothing about how the bulk of the data is distributed. It is also completely at the mercy of a single unusual value: one outlier at either end changes the range entirely while leaving the rest of the data untouched.
Example 1.29. Find the range of the following distribution. \[20,\quad 23,\quad 30,\quad 33,\quad 21,\quad 19,\quad 28,\quad 36,\quad 32,\quad 25,\quad 29\]
Solution. The largest value is \(36\) and the smallest is \(19\), so \[\text {Range}=36-19=17.\] Note how little work the other nine observations did: the same range would result if every one of them were replaced by \(25\).
Questions on this section
Stuck on something here? Ask below and it stays attached to this topic.