From this example, it can be seen that to reach valid conclusions it is important to measure
how data are dispersed around the measure of central tendency.
Dispersion is important, not merely as a supplement to the mean, but also as a significant
item in itself. The performance of a student is judged not only by his average but also by his
consistency. When a measure of central tendency and a measure of dispersion have been
computed for a series, generally the two most important characteristics have been summarized.
The first measure of dispersion that we will examine is the range. The range is the difference
between the highest and lowest values in a group of observations. In the example above, the
range of Group A is 10,000 -1,000 9,000, and the range of Group B is 4,500 -2,500 = 2,000. This
quickly illustrates that Group B's wages vary much less than Group A's wages.
Generally it is desirable to express the range in terms of the upper and lower limits; thus, we
would say A's range is
,000 to ,000 and B's is ,500 to ,500. This gives the reader an
idea of the general location of the data.
Although it has the merit of being simple, the range is a rather unsatisfactory measure
because it is determined only by the two extreme values in a group of observations, the high and
the low. Since these two figures are only "boundaries" of the rest of the data, they are insensitive
to the behavior or location of figures between them. The range should be used only in cases
where a quick, cursory look at the data is desired.
Find the range of the following costs:
Range = _________________