Question

Find the mode of the following distribution :
Marks : 0 -10 10-20 20 - 30 30 – 40 40 - 50 50 - 60
Number of students:
4 6 7 12 5 6
​

Answer 1

Answer:

The mode of given data  is 34.17

Step-by-step explanation:

Given  data

 marks               0-10     10-20     20-30    30-40    40-50     50-60

 number of          4            6             7           12           5               6

 students

⇒ here the highest frequency is 12 , thus the class 20-30 is the modal  

     class  from this we will calculate the mode of the given data

     the formula to find the mode for a grouped data is given

                  mode =  $l + [ \frac{f_{1}-f_{0} }{2(f_{1})-f_{0} -f_{2} } ]h$    

here   $l$ = lower limit of the modal class = 30

          $f_{1}$ = frequency of modal class =  12

         $f_{0}$ = frequency of the class before the modal class =  7

        $f_{2}$ = frequency of the class after the modal class =5

        h = size of class interval = 10

          mode =  $30 + [ \frac{12-7}{2(12) - 7- 5} ]10$  

                    = $30 + [ \frac{5(10)}{ 24 - 12} ]$

                    = 30 + $\frac{50 }{12}$  

                    = 30 + 4.17

                     = 34.17  

Answer 2

Answer:

The Mode of the Following distribution is 34.166.

Step-by -step explanation:

In context to the given question , we have to find the Mode of the given distribution

Given  data

Marks            Frequency of Number of students

0-10                  4

10-20                6

20-30                7

30-40                12     ⇔ HIGHEST FREQUENCY(MODAL CLASS)

40-50                5

50-60                6

Mode =  L + h  $\frac{f(m) - f(p)}{(f(m) - f(p))+(f(m) - f(s))}$

 

Where;

⇒ L = lower limit of the modal class = 30

⇒ h = size of class interval = 10

⇒ f(m)   = frequency of modal class =  12

⇒ f(p)     = frequency of the class preceding( before)the modal class =7

⇒ f (s)   = frequency of the class succeeding (after) the modal class =5

Therefore, By putting the known values we get,

Mode =  30 + 10 $\frac{12-7}{(12-7)+(12-5)}$

Mode =  30 + 10 $\frac{5}{5+7}$

Mode =  30 + 10 $\frac{5}{12}$

Mode =  30 + 10 (0.4166)

Mode =  30 + 4.166

Mode =  34.166

∴ The Mode of the Following distribution is 34.166