Krishna
1

Step 1: Recall the mode formula for the grouped data

            

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


                Where,

                        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 8, and the class corresponding to this

             frequency is 3-5.

                        So, the modal class is 3-5.


                                    lower boundary l = 3

                                Class size h = 5 - 3 = 2      

                        The frequency of modal class   f_1  = 8

          The frequency of the class preceding the modal class f_0  = 7  

          The frequency of the class succeeding the modal class. f_2 = 2


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


                              =   3 + \frac{8 - 7}{2*8 - 7 - 2} * 2


                              =   3 + \frac{1}{7} * 2


                              =  3 + 0.2857


                              =  3.286


                    Hence, mode = 3.286