Question

Draw an ogive for the data given below and from the graph determine:  

1. the median marks
2. the number of students who obtained more than 75% marks 

Marks	No. of students
0 – 9	5
10 – 19	9
20 – 29	16
30 – 39	22
40 – 49	26
50 – 59	18
60 – 69	11
70 – 79	6
80 – 89	4
90 – 99	3

Answer 1

Marks	No. of students	Cumulative frequency
0.5 – 9.5	5	5
9.5 – 19.5	9	14
19.5 – 29.5	16	30
29.5 – 39.5	22	52
39.5 – 49.5	26	78
49.5 – 59.5	18	96
59.5 – 69.5	11	107
69.5 – 79.5	6	113
79.5 – 89.5	4	117
89.5 – 99.5	3	120

Total number of terms = 120  

i. i. ∴ Median = `120/2` = 60^th term 

Through mark 60, draw a parallel line to x-axis which meets the curve at A. From A, draw a perpendicular to x-axis meeting it at B. 

The value of point B is the median = 43 

ii. Total marks = 100 

75% of total marks = `75/100 xx 100 = 75` 

The number of students getting more than 75% marks = 120 – 111 = 9