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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
Solution
|
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
= 20.5th term
Which is between 15 and 25.
∴ Median = 6
(ii) Mode frequency of 6 is the highest.
∴ Mode = 3
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