Question

Find the mode of the following frequency distribution: Marks 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 Number of students 15 30 45 12 18

Answer 1

Answer:

33.12

Step-by-step explanation:

Given Find the mode of the following frequency distribution: Marks 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 Number of students 15 30 45 12 18

 Marks                           no of students

10--20                                 15

20---30                                30

30--40                                  45

40--50                                  12

50--60                                   18

We have maximum frequency f = 45, so the modal class is 30--40, the first term of modal class is l = 30, the previous term of maximum frequency is    f1 = 30 and the next term of maximum frequency is f2 = 12, and h = 10(interval of marks)

We have the formula Mode = l + h(f - f1 / 2f - f1 - f2)

                                            = 30 + 10(45 - 30 /2(45) - 30 - 12)

                                           =   265 / 8

                                Mode = 33.12

Answer 2

Answer:

Mode of the sample is 33.12

Step-by-step explanation:

Given:

We are given with the frequency distribution which can be written as

 Marks                           Number of students

10--20                                 15

20---30                                30

30--40                                  45

40--50                                  12

50--60                                   18

To Find:

Mode = ?

Solution:

When in a frequency distribution we have to find the mode so we look at the values with most frequency because they have occurred mostly

We have maximum frequency f = 45,

so

the modal class is 30--40,

Now first term of model class = l  = 30

Previous term of max frequency =f1 =  30

Next term of max frequency =f2 = 12

Interval = 40 -30 = 10

Now the formula for finding the mode is

Mode =$l+h(f-\frac{f1}{2f}-f1-f2)$

Putting in the values we get

           = $30+10(45-\frac{30}{2(45)}-30-12)$

It becomes

            =   265 / 8 

Mode = 33.12

So Mode of given is 33.12