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Question
Mrs. Garg recorded the marks obtained by her students in the following table. She calculated the modal marks of the students of the class as 45. While printing the data, a blank was left. Find the missing frequency in the table given below.
| Marks Obtained |
0 − 20 | 20 − 40 | 40 − 60 | 60 − 80 | 80 − 100 |
| Number of Students |
5 | 10 | − | 6 | 3 |
Solution
Modal class is 40 − 60, `l` = 40, `h` = 20, `f_1` =?, `f_0` = 10, `f_2` = 6
45 = `40 + 20 xx [(f_1 - 10)/(2f_1 - 10 - 6)]`
⇒ `1/4 = (f_1 - 10)/(2f_1 - 16)`
⇒ `2f_1 - 16 = 4f_1 - 40`
⇒ `f_1` = 12
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