Two important measurements of a data set include the center of the data and the spread of the data. The center can be measured in a number of ways. The most popular of these are the mean, median, mode and midrange. In a similar fashion there are different ways to calculate how spread out the data set is. The easiest and crudest measure of spread is called the range.
Formula for Range
The calculation of the range is very straightforward. All we need to do is find the difference between the largest data value in our set and the smallest data value. Stated succinctly we have the following formula:
Range = Maximum Value – Minimum Value.
For example, the data set 4,6,10, 15, 18 has maximum of 18, minimum of 4 and range of 18 – 4 = 14.
Limitations of Range
The range is a very crude measurement of the spread of data because it is extremely sensitive to outliers. A single data value can greatly affect the value of the range. For example, consider the set of data 1, 2, 3, 4, 6, 7, 7, 8. The maximum value is 8, the minimum is 1 and the range is 7. Now consider the same set of data, only with the value 100 included. The range now becomes 100 – 1 = 99. The addition of a single extra data point greatly affected the value of the range. The standard deviation is another measure of spread that is less susceptible to outliers. The drawback is that the calculation of the standard deviation is much more complicated.
Applications of Range
The range is a good way to get a very basic understanding of how spread out our data are. The range can be used to estimate the standard deviation by use of the range rule. The range also occurs in a boxplot. The maximum and minimum values are both graphed at the end of the whiskers of the graph. The total length of the whiskers and box is equal to the range.