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 61, and the class corresponding to this

          frequency is 60 - 80,

                            So, the modal class is 60 - 80.

                                        lower boundary l = 60

                                                Class size h = 80 - 60 = 20

               The frequency of modal class f_1 = 61

               The frequency of the class preceding the modal class f_0 = 52

            The frequency of the class succeeding the modal class. f_2 = 38


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


                               = 60 + \frac{61 - 52}{2*61 - 52 - 38} * 20


                               = 60 + \frac{9}{32} * 20

  

                               = 60 + \frac{9}{8} * 5


                               = 60 + 5.625


                               = 65.625


                       Hence, mode = 65.625