In an annual examination, marks (out of 90) obtained by students of Class X in mathematics are given below:
Marks obtained | 0 - 15 | 15 - 30 | 30 - 45 | 45 - 60 | 60 - 75 | 75 - 90 |
Number of students | 2 | 4 | 5 | 20 | 9 | 10 |
Find the mean marks.
We will find the mean marks using step - deviation method, where A = Assumed mean and h = length of class interval.
Here, let A = 37.5 and h = 15
MARKS OBTAINED | MID - POINT(xi) | DEVIATION(di) di = xi – 37.5 | NUMBER OF STUDENTS(fi) | ui = di/h | fiui |
0 - 15 | 7.5 | - 30 | 2 | - 2 | - 4 |
15 - 30 | 22.5 | - 15 | 4 | - 1 | - 4 |
30 - 45 | 37.5 = A | 0 | 5 | 0 | 0 |
45 - 60 | 52.5 | 15 | 20 | 1 | 20 |
60 - 75 | 67.5 | 30 | 9 | 2 | 18 |
75 - 90 | 82.5 | 45 | 10 | 3 | 30 |
TOTAL | 50 | 60 |
We have got
A = 37.5, h = 15, Σfi = 50 & Σfiui = 60
∵ mean is given by
⇒ 
⇒ 
Thus, mean marks are 55.5.
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