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 20, and the class corresponding to this

          frequency is 40 - 50,

                           So, the modal class is 40 - 50.

                                       lower boundary l = 40

                                              Class size h = 50 - 40 = 10

             The frequency of modal class f_1 = 20

            The frequency of the class preceding the modal class f_0 = 12

            The frequency of the class succeeding the modal class. f_2 = 11


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


                          = 40 + \frac{20 - 12}{2*20 - 12 - 11} * 10


                          = 40 + \frac{8}{17} * 10

                          = 40 + 0.470588 * 10


                          = 40 + 4.7058


                          = 44.7058


                 Hence, mode = 44.7058