Question

The marks obtained by 120 students in a 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 an ogive for the given distribution on a graph sheet.

Use a suitable scale for ogive to estimate the following:
(1) The median.
(2) The number of students who obtained more than 75% marks in the test.
(3) The number of students who did not pass the test if minimum marks required to pass is 40

Answer 1

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

`n = 120/2 = 60`

1) Through marks 60, draw a line segment parallel to x-axis which meets the curve at A. From A, draw a line perpendicular to x-axis meeting at B. Median = 43

2) Through marks 75, draw a line segment parallel to y-axis which meets the curve at D. From D, draw a line perpendicular to y-axis which meets y-axis at 110.

Number of students getting more than 75% = 120 - 110 = 10 students

3) Through marks 40, draw a line segment parallel to y-axis which meets the curve at C. From C, draw a line perpendicular to y-axis which meets y-axis at 52.

The number of students who did not pass = 52.