Question

Given below is the distribution of weekly pocket money received by students of
a class. Calculate the modal pocket money that is received by most of the students.
Pocket Money. No. of students
0-20. 2
20-40. 2
40-60. 3
60-80. 12
80-100. 18
100-120. 5
120-140. 2

80-90.

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Answer 1

Here is your needful answer....... Hope this will help you.....

Answer 2

Modal pocket money that is received by most of the students is 86.32.

Step-by-step explanation:

We are given below the distribution of weekly pocket money received by students of  a class;

                    Pocket Money            No. of students (f)      

                           0 - 20                                 2

                          20 - 40                                2

                          40 - 60                                3

                         60 - 80                                12

                         80 - 100                               18

                        100 - 120                                5

                        120 - 140                                2

Now, firstly after observing our data we have to find the frequency which is maximum in our data, that is the highest frequency in our data is 18.

So, the corresponding class interval with respect to frequency 18 is 80 - 100, that means that the modal class is 80 - 100.

Now, the formula for calculating mode is given by;

                Mode =  $L+\frac{f_1-f_0}{(f_1-f_0)+(f_1-f_2)} \times h$

where,  L = lower limit of modal class = 80

             $f_1$ = frequency of modal class = 18

             $f_0$ = frequency just above the modal class frequency = 12

             $f_2$ = frequency just below the modal class frequency = 5

              h = width of class interval = 20

Now,  Mode  =  $80+\frac{18-12}{(18-12)+(18-5)} \times 20$

                      =  80 + 6.316

                      =  86.32

Therefore, the modal pocket money that is received by most of the students is Rs 86.32.