The marks obtained by 120 students in a Mathematics test are given below :

Marks	No. of students
0-10	5
10-20	9
20-30	16
30-40	22
40-50	26
50-60	18
60-70	11
70-80	6
80-90	4
90-100	3

Using the informations, given above draw an ogive on a graph sheet. Take a suitable scale for your ogive. Use the ogive to drawn to estimate :

(i) the median marks.

(ii) the number of students who obtained more than 75% marks in the test.

(iii) the number of students who did not pass in the test if the pass percentage was 40.

Cumulative frequency distribution table :

(i) Here, n = 120, which is even.

By formula,

Median = $\dfrac{n}{2}$ th term

= $\dfrac{120}{2}$ = 60th term.

Steps of construction :

1. Take 1 cm along x-axis = 10 units.

2. Take 1 cm along y-axis = 20 units.

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

4. Plot the points (10, 5), (20, 14), (30, 30), (40, 52), (50, 78), (60, 96), (70, 107), (80, 113), (90, 117) and (100, 120).

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

6. Draw a line parallel to x-axis from point L (no. of students) = 60, touching the graph at point M. From point M draw a line parallel to y-axis touching x-axis at point N.

From graph, N = 43

Hence, median = 43.

(ii) Total marks = 100.

75% marks = $\dfrac{75}{100} \times 100$ = 75.

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 = 110.

∴ 110 students score less than or equal to 75%.

Students scoring above than 75% = 120 - 110 = 10.

Hence, 10 students score more than 75%.

(iii) Total marks = 100.

40% marks = $\dfrac{40}{100} \times 100$ = 40.

Draw a line parallel to y-axis from point R (marks) = 40, touching the graph at point T. From point T draw a line parallel to x-axis touching y-axis at point S.

From graph, S = 52.

∴ 52 students score less than or equal to 40%.

Hence, 52 students failed the test.