Krishna
0

Step 1: Set up a cumulative frequency distribution table

             NOTE: The cumulative frequency is calculated using a frequency

                           distribution table.

                              


Step 2: Calculate the median class of the data.

             NOTE: Locate the class whose cumulative frequency exceeds \frac{n}{2} for the  first time. This is called the median class.

                   The total number of observations n = 30

                                   \frac{n}{2}=\frac{30}{2} = 15

​               55 - 60 is the class whose cumulative frequency is 6 greater than (and nearest to) \frac{n}{2}, i.e.,15


              Therefore, 55 - 60 is the median class      


Step 3: Substitute that values in the median formula

           From the table;

                l = lower boundary of median class = 55,

               n = number of observations = 30,

               cf = cumulative frequency of class preceding the median class = 13

                 f = frequency of median class = 6

                h = class size (size of the median class) = 60 - 55 =.5


              Substituting the values


                                  Median = l + \frac{\frac{n}{2}-cf}{f}*h

                                              Median = 55 + \frac{15 - 13}{6}*5

                                                                 =   55 + \frac{5}{3}

  


                                           Hence, the median = 56.67