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 10 , and the class corresponding

             to this frequency is 30 - 35.

                         So, the modal class is 30 - 35.

                             lower boundary l = 30

                                     Class size h = 35 - 30 = 5

                   The frequency of modal class f_1 = 10


            The frequency of the class preceding the modal class f_0 = 9


            The frequency of the class succeeding the modal class. f_2 = 3


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


                             = 30 + \frac{10 - 9}{2*10 - 9 - 3} * 5


                            = 30 + \frac{1}{8} * 5

                            = 30 + 0.625


                           = 30.625


                  Hence, mode = 30.625.




Step 4: Calculate the mean of the given data



         Mean: The mean (or average) of observations is the sum of the values of

          all  the observations divided by the total number of observations.


              Step deviation method

                       x_i is the class mark = Average of the boundaries(class intervals)

                          Assumed value a = middle value of the observations = 32.5


                                     Deviation d_i = x_i - a

                             Step deviation u_i = \frac{d_i}{h}


                       h = size of the class = 35 - 30= 5


              Sum of the values of all the observations \Sigma f_ix_i = -23\Sigma f_iu_i=-23

                                    Total number of observations \Sigma f_i = 35

                Substitute all the values in the values in the step deviation formula


                          Formula: Mean = a + \frac{\Sigma f_iu_i}{\Sigma f_i}*h


                                                  = 32.5 + \frac{-23}{35}*5


                                                  = 32.5 - \frac{23}{7}


                                                  = 29.22


                                       Mean = 29.22