Theory:

Consider the following example:
 
Ram has gone out walking every day. In the first two weeks, he has walked the following distances on each of the days.
 
\(4\), \(5\), \(7\), \(2\), \(6\), \(7\), \(5\), \(4\), \(7\), \(6\), \(4\), \(3\), \(5\) and \(4\) miles respectively.
 
Construct a frequency distribution table and find the range of the data collected.
 
Step \(1\): Let us arrange the numbers in ascending or descending order.
 
\(2\), \(3\), \(4\), \(4\), \(4\), \(4\), \(5\), \(5\), \(5\), \(6\),\(6\), \(7\), \(7\), \(7\)
 
Step \(2\): Let us construct a frequency distribution table of the ordered data.
 
Distance
(in miles)
Frequency
\(2\)
\(1\)
\(3\)
\(1\)
\(4\)
\(4\)
\(5\)
\(3\)
\(6\)
\(2\)
\(7\)
\(3\)
 
Step \(3\): Find the range of the data.
 
From the tabular column, the highest value is \(7\), and the lowest value is \(2\).
 
\(\text{Range} = \text{Highest value} - \text{Lowest value}\)
 
\(= 7 - 2\)
 
\(= 5\)
 
The range of the given set of data is \(5\).