Krishna
0

Step 1: Recall the formula of the median for grouped data.

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


                          where, l = lower boundary of median class,

                                    n = number of observations,

                              cf = cumulative frequency of class preceding the median class,

                                f = frequency of median class,

                                h = class size (size of the median class).


Step 2: Set up a cumulative frequency distribution table

             NOTE: The cumulative frequency is calculated using a frequency

                         distribution table.

                        



Step 3: 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 = 100

                                                                          \frac{n}{2}=\frac{100}{2}

                125 - 145 is the class whose cumulative frequency is 86  greater than

                (and nearest to) \frac{n}{2}, i.e., 50.


                  Therefore, 35 - 45 is the median class


Step 4: Substitute that values in the median formula

              From the table;

                    l = lower boundary of median class = 35,

                    n = number of observations = 100,

                  cf = cumulative frequency of class preceding the median class = 45

                  f = frequency of median class = 33

                  h = class size (size of the median class) = 20 - 15 = 5.


                    Substituting the values


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


                                        Median = 35 + \frac{50 - 45 }{33}*5


                                                      = 35 + \frac{25}{33}


                                                      = 35 + 0.75

                                    Hence, the median = 35.75