Question

Using a graph paper, draw a histogram and estimate the mode for the following frequency distribution: [3] Class interval 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 Frequency 2 8 10 5 4 3

Answer 1

The mode for the given data is 20.86.

Step-by-step explanation:

We are given with the following frequency distribution data;

        Class Interval                            Frequency (f)

              0 - 10                                            2

             10 - 20                                           8

             20 - 30                                         10

             30 - 40                                          5

             40 - 50                                          4

             50 - 60                                          3

Firstly, it is clear from the data that the highest frequency is 10, this means that the modal class of our data is 20 - 30.

Now, the formula for finding the mode of any grouped frequency distribution is given by;

               Mode  =  $x_L+\frac{f_m-f_m_-_1}{(f_m-f_m_-_1)+(f_m-f_m_+_1)} \times h$

where, $x_L$ = lower limit of the modal class = 20

            $f_m$ = frequency of the modal class = 10

            $f_m_-_1$ = frequency just above the modal class = 8

           $f_m_+_1$ = frequency just below the modal class = 5

               h = width of the class interval = 10

So, Mode  =  $20+\frac{10-8}{(10-8)+(10-5)} \times 10$

                 =  $20+\frac{2}{2+5} \times 10$

                 =  20 + 2.86 = 20.86 ≈ 21.

Hence, the mode for the given frequency distribution is 20.86.