Question

The marks obtained by 45 students of a class in a test are given below:

Marks	40-45	45-50	50-55	55-60	60-65	65-70
Number of students	8	9	10	9	5	4

Find the mean and median marks.

Answer 1

We have,

Marks	Number of students (fi)	Mid-point (xi)	xi fi	cf
40-45	8	42.5	340	8
45-50	9	47.5	427.5	17
50-55	10	52.5	525	27
55-60	9	57.5	517.5	36
60-65	5	62.5	312.5	41
65-70	4	67.5	270	45
	`sum fi = 45`		`sum fi  x i = 2392.5`

Mean = `(sum fi xx xi)/(sum fi)`

= `2392.5/45`

= 53167

Since, N = 45 ⇒ `N/2 = 45/2` = 22.5

Which lies in the class interval 50-55.

Here, l = 50, h = 5, f = 10, cf = 17

Median = `l + [( N/2 - cf)/f] xx h`

= `50 + [(225 - 17)/10] xx 5`

= 52.75

Therefore, mean is 53.167 and median marks is 52.75.