Range is defined as the difference between the maximum and minimum values of the data. Although Range is the simplest measure of dispersion and is easy to calculate but it is not a good measure of dispersion because it ignores variation among all other values and depends upon only two extreme values. However if there is a lack of time or the observations are homogenous then range is a good measure of dispersion to use. The calculation of range for grouped and ungrouped data is elaborated with the help of simple problems given below.
Range of Ungrouped Data
Problem: The following data show the weights (in pounds) of 25 boys: 108, 104, 120, 108, 110, 125, 103, 112, 99, 115, 114, 96, 116, 100, 129, 117, 119, 121, 112, 111, 120, 111, 121, 101, and 109, Find the range of data.
Arrange Data in Ascending Order:
96, 99, 100, 101, 103, 104, 108, 108, 109, 110, 111, 111, 112, 112, 114, 115, 116, 117, 119, 120, 120, 121, 121, 125, 129
Range of Frequency Distribution
In a frequency distribution range is the difference between upper class boundary of the last interval and lower class boundary of the first interval.
Problem: For the following frequency distribution, calculate the range.
Solution:
We know that:
Range = Upper class boundary of last interval – Lower class boundary of first interval
Therefore,