Krishna
0

Step 1: Recall the mode formula for the grouped data


                     Mode = l + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} * h


                            l - The lower boundary of the modal class,

                            h - The class size,

                           f_1 - The frequency of modal class,

                           f_0 - the frequency of the class preceding the modal class,

                           f_2 - the frequency of the class succeeding the modal class.


Step 2: Identify the modal class and locate the values of the frequencies.

            NOTE: Locate a class with the maximum frequency, called the modal class.

                        (The mode is a value inside the modal class)


          Here the maximum class frequency is 18, and the class corresponding to this

          frequency is 4000 - 5000,

                          So, the modal class is 4000 - 5000.

                                            lower boundary l = 4000

                                                   Class size h = 5000 - 4000 = 1000

                                The frequency of modal class f_1 = 18

            The frequency of the class preceding the modal class f_0 = 4

          The frequency of the class succeeding the modal class. f_2 = 9


Step 3: Substitute the values in the formula and calculate the mode.


                      Mode = l + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} * h


                               = 4000 + \frac{18 - 4}{2*18 - 4 - 9} * 1000


                               = 4000 + \frac{14}{23} * 1000

                              = 4000 + 0.608695 *1000


                              = 4000 + 608.695


                              = 4608.695

                      Hence, mode = 4608.695