Question

The marks obtained by 100 students in a Mathematics test are given below:

Marks	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90	90-100
No. of Students	3	7	12	17	23	14	9	6	5	4

Draw an ogive for the given distribution on a graph sheet.

Use a scale of 2 cm = 10 units on both axes.

Use the ogive to estimate the :

1. median.
2. lower quartile.
3. number of students who obtained more than 85% marks in the test.
4. number of students who did not pass in the test if the pass percentage was 35.

Answer 1

Marks	C.F.	Points
Less than 10	3	(10, 3)
Less than 20	10	(20, 10)
Less than 30	22	(30, 22)
Less than 40	39	(40, 39)
Less than 50	62	(50, 62)
Less than 60	76	(60, 76)
Less than 70	85	(70, 85)
Less than 80	91	(80, 91)
Less than 90	96	(90, 96)
Less than 100	100	(100, 100)

i. Median = `("n"/2)^"th"` observation

= `(100/2)^"th"` observation

= 50^th observation

= 45

ii. Lower Quartile (Q₁) = `("N"/2)^"th"` observation

= `(100/4)^"th"` observation

= 25^th observation

= 32

iii. Number of students who obtained more than 85% marks

= (100 – 94)

= 6

iv. Number of students who did not pass if passing % of marks is 35 = 30