Step 1:  Find the median of the given data

          Skill 1: Set up a cumulative frequency distribution table

                        NOTE: The cumulative frequency is calculated using a frequency

                          distribution table.

          Skill 2: Calculate the median class of the data.

                        NOTE: Locate the class whose cumulative frequency exceeds

                        \frac{n}{2}   for the first time. This is called the median class.

                              The total number of observations n = 68. So, \frac{n}{2} = 34

                      125 - 145 is the class whose cumulative frequency is 42 greater than

                      (and nearest to) \frac{n}{2}, i.e., 25.5.

                                  Therefore, 125 - 145 is the median class

          Skill 3: Substitute that values in the median formula

                          From the table;  

                           l = lower boundary of median class = 125,

                          n = number of observations = 68,

                         cf = cumulative frequency of class preceding the median class =13

                          f = frequency of median class = 20

                         h = class size (size of the median class) = 145 - 125 = 20.  

                 Substituting the values

                            Median=l+\frac{\frac{n}{2}-cf}{f}*h

                              Median = 125 + \frac{34 - 22}{20}*20

                                    = 125 + 12

                                    = 137

                          Hence, the median = 137

Step 2: Find the mode of the given data

            Skill 1: 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 125 - 145.

                      So, the modal class is 125 - 145.

                              lower boundary l = 125

                              Class size        h = 145 - 125 =20

                              The frequency of modal class f_1 = 20

                  The frequency of the class preceding the modal class     f_0 = 13

                  The frequency of the class succeeding the modal class. f_2 = 14

            Skill 2: Substitute the values in the formula and calculate the mode.

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

                                                  = 125 + \frac{20 - 13}{2*20 - 13 - 14} * 20

                                                = 125 + \frac{7}{13} * 20

                                                = 125 + 10.77

                                                = 135.77

                                  Hence, mode = 135.77

Step 3: Calculate the mean of the given data

            Skill 1: Choose one among the observations as the assumed mean, and

            Find the deviation and step deviation of ‘a’ from each of the observations

            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 = 135

                                          Deviation d_i = x_i - a

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

                              h = size of the class = 85 - 65 = 20

                  Sum of the values of all the observations \Sigma f_iu_i = 7

                                        Total number of observations \Sigma f_i = 68

          Skill 2:  Substitute all the values in the values in the step deviation formula

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

                                                    = 135 + \frac{7}{68}*20

                                                    = 135 - \frac{140}{68}

                                                    = 135 + 2.05

                            Hence, Mean = 137.05      

Step 4: Compare the mean, mode and median

              Mean = 137.05, mode = 135.77  median = 137

              Mean, mode and median are almost similar