3.1 The range
The range is defined below.
The range is the distance between the lower and the upper extremes. It can be calculated from the formula:
where is the upper extreme and is the lower extreme.
Given an ordered batch of data, for example in a stemplot, the range can easily be calculated. However, the range tells us very little about how the values in the main body of the data are spread. It is also very sensitive to changes in the extreme values, like those considered in Subsection 1.4. It would be better to have a measure of spread that conveys more information about the spread of values in the main body of the data. One such measure is based upon the difference between two particular values in the batch, known as the quartiles. As the name suggests, the two quartiles lie one quarter of the way into the batch from either end. The major part of the next subsection describes how to find them.