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

Answer 1

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