Question

Marks obtained by 200 students in an examination are given below:

Marks	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70	70 - 80	80 - 90	90 - 100
Frequency	5	11	10	20	28	37	40	29	14	6

Draw an ogive for the given distribution taking 2 cm = 10 marks on one axis and 2 cm = 20 students on the other axis. Using the graph, determine:
(i) The median marks
(ii) The number of students who failed if minimum marks required to pass is 40.
(iii) If scoring 85 and more marks is considered as grade one, find the number of students who secured grade one in the examination.

Answer 1

On graph

Marks	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70	70 - 80	80 - 90	90 - 100
f	5	11	10	20	28	37	40	29	14	6
c.f.	5	16	26	46	74	111	151	180	194	200

(i) Median = `("n"/2)^"th" "obv" = (200/2)^"th" "obv"`.
= 100^th obv.
= 57
(ii) No. of students who failed = 46
(iii) No. of students who secured grade one = 200 - 188 = 12.