Theory:

Problem \(1\)
Find the mode of the following numbers.
 
\(70\), \(50\), \(90\), \(50\), \(40\), \(20\), \(10\), \(50\), \(60\), \(80\), \(30\), \(50\), \(30\)
 
Let us now find the solution.
 
Step \(1\): Arrange the numbers in the ascending order.
 
\(10\), \(20\), \(30\), \(30\), \(40\), \(50\), \(50\), \(50\), \(50\), \(60\), \(70\), \(80\), \(90\)
 
Step \(2\): Find the number that occurs for the most number of times.
 
\(50\) occurs the most number of times.
 
Therefore, \(50\) is the mode of that set of data.
 
Problem \(2\)
Find the mode of the following numbers.
 
\(15\), \(12\), \(8\), \(3\), \(5\), \(7\), \(15\), \(3\), \(9\), \(8\), \(2\), \(8\), \(15\)
 
Let us now find the solution.
 
Step \(1\): Arrange the numbers in the ascending order.
 
\(2\), \(3\), \(3\), \(5\), \(7\), \(8\), \(8\), \(8\), \(9\), \(12\), \(15\), \(15\), \(15\)
 
Step \(2\): Find the number that occurs for the most number of times.
 
Both \(8\) and \(15\) occur thrice.
 
Therefore, \(8\) and \(15\) are the modes of that data.
 
In other words, the given set of data is bimodal.