Question

In a case of 40 students, marks obtained by the students in a class test (out of 10) are given below:

Marks	1	2	3	4	5	6	7	8	9	10
Number of students	1	2	3	3	6	10	5	4	3	3

Calculate the following for the given distribution:
(i) Median
(ii) Mode

Answer 1

Marks (x)	No.of Students	c.f
1	1	1
2	2	3
3	3	6
4	3	9
5	6	15
6	10	25
7	5	30
8	4	34
9	3	37
10	3	40
Total	40

 

 

 

 

 

 

 

 

 

 

 

 

 

(i) Total number of Students = 40 which is even

   Median =`1/2[(n/2)+(n/2+1)^(th) "term"]`

                = `1/2[(40/2)+(40/2+1)"term"]`

                =`1/2[20^(th) " term" + 21^(th)" term"]`

                =`(41/2)^(th) ` term

                = 20.5^th term 

  Which is between 15 and 25.

 ∴ Median = 6
(ii) Mode frequency of 6 is the highest.
∴  Mode  = 3