The result of a examination is tabulated below :

Marks (less than)	No. of candidates
10	0
20	25
30	42
40	65
50	95
60	120
70	128
80	135
90	148
100	150

Draw the ogive for the above data and from it determine :

(i) the number of candidates who got marks less than 45.

(ii) the number of candidates who got marks more than 75.

The above table can be written as :

Steps of construction :

1. Take 1 cm = 10 marks on x-axis.

2. Take 1 cm = 20 students on y-axis.

3. Plot the point (0, 0) as ogive starts on x-axis representing lower limit of first class.

4. Plot the points (10, 0), (20, 25), (30, 42), (40, 65), (50, 95), (60, 120), (70, 128), (80, 135), (90, 148) and (100, 150).

5. Join the points by a free-hand curve.

6. Draw a line parallel to y-axis from point L (marks) = 45, touching the graph at point M. From point M draw a line parallel to x-axis touching y-axis at point N.

From graph, N = 80

Hence, no. of students having marks less than 45 = 80.

(ii) Steps :

1. Draw a line parallel to y-axis from point O (marks) = 75, touching the graph at point P. From point P draw a line parallel to x-axis touching y-axis at point Q.

From graph, Q = 131

It means that,

131 students have marks less than or equal to 75.

∴ No. of students having marks more than 75 = 150 - 131 = 19.

Hence, no. of students having marks more than 75 = 19.