Question

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

Marks	No. of students
0 – 10	5
10 – 20	11
20 – 30	10
30 – 40	20
40 – 50	28
50 – 60	37
60 – 70	40
70 – 80	29
80 – 90	14
90 – 100	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:

1. The median marks.
2. The number of students who failed if minimum marks required to pass is 40.
3. If scoring 85 and more marks are considered as grade one, find the number of students who secured grade one in the examination.

Answer 1

Marks	No. of students (f)	cf
0 – 10	5	5
10 – 20	11	16
20 – 30	10	26
30 – 40	20	46
40 – 50	28	74
50 – 60	37	111
60 – 70	40	151
70 – 80	29	180
80 – 90	14	194
90 – 100	6	200

The ogive can be drawn as follows:

i. Median marks will be 57.5 as the x coordinate corresponding to n/2 i.e., 100 is 57.5.

ii. The number of students who failed (if minimum marks required to pass is 40) = 46 (approx from the graph)

iii. Number of students who secured more than 85 marks (grade one) = Total number of students – 188 = 200 – 188 = 12