Question

Attempt this question on graph paper. Marks obtained by 200 students in 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
No. of students	5	10	14	21	25	34	36	27	16	12

Draw an ogive for the given distribution taking 2 cm = 10 makrs on one axis and 2 cm = 20 students on the other axis.
From the graph find:
(i) the median
(ii) the upper quartile
(iii) number of student scoring above 65 marks.
(iv) If to students qualify for merit scholarship, find the minimum marks required to qualify.

Answer 1

Marks	No. of Students	c.f.	Points
0 - 10	5	5	(10, 5)
10 - 20	10	15	(20, 15)
20 - 30	14	29	(30, 29)
30 - 40	21	50	(40, 50)
40 - 50	25	75	(50, 75)
50 - 60	34	109	(60, 109)
60 - 70	36	145	(70, 145)
70 - 80	27	172	(80, 172)
80 - 90	16	188	(90, 188)
90 - 100	12	200	(100, 200)
	n = 200

(i) Let A be the point on y-axis representing frequency
Here, n (no. of student) = 200 (even)
Median = `("n"/2)^"th" "term"`
= `(200/2)^"th" "term"`
= 100^th term
From the graph 100th term = 57·5
(ii) Upper quartile = `(3"n")/(4)`
= `(3 xx 200^"th")/(4)"term"`
= `(600)/(4)` = 150^th term
From graph 150^th term
The upper quartile = 72
(iii) No. of students scoring above 65 marks
⇒ Total No. of students - No. of students scoring ≤ 65 marks
⇒ 200 - 126
⇒ 74 (approx.)
(iv) From the above diagram, we observe the students from 191 to 200 qualify for merit scholarship.
∴ The student who qualifies for merit scholarship scores more than 91 marks.
∴ The minimum marks required to qualify for merit scholarship = 92 (approx.).