Question

Use graph paper for this question. 
The marks obtained by 120 students in an English 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	5	9	16	22	26	18	11	6	4	3

Draw the ogive and hence, estimate:
(i) the median marks.
(ii) the number of students who did not pass the test if the pass percentage was 50.
(iii) the upper quartile marks.

Answer 1

C.I	Marks less than	No.of students	Cumulative frequency
0-10	10	5	5
10-20	20	9	14
20-30	30	16	30
30-40	40	22	52
40-50	50	26	78
50-60	60	18	96
60-70	70	11	107
70-80	80	6	113
80-90	90	4	117
90-100	100	3	120

i. No.of students =120
∴ Median = 60th term through marks of 60 draw a line parallel to x - axis which meets the curve at A. From A draw perpendicular to x-axis, which meets it at A . From A draw a perpendicular to x-axis which
meets it at B.
ii. The upper quartile marks `(Q_3 ) = 3/4 n^(th)` term

`= 3^(th)/4 xx 120= 90^(th) ` term

draw a line parallel to x-axis which meets the 1 curve at C. From C draw perpendicular to x-axis which meets it at D.