Use graph (squared paper) to solve this question.

(i) Draw the ogive for the following frequency distribution.

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

Use your graph to find :

(ii) the median

(iii) the number of students who secured more than 75% marks.

(i) The class intervals are discontinuous.

By formula,

Adjustment factor

$= \dfrac{\text{Lower limit of class - Upper limit of preceding class}}{2} \\[1em] = \dfrac{20 - 19}{2} \\[1em] = \dfrac{1}{2} \\[1em] = 0.5$

New lower class limit = Lower class limit - Adjustment factor

New upper class limit = Upper class limit + Adjustment factor

Steps of construction :

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

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

3. A kink is drawn near x-axis to show that the scale begins at 9.5

4. Plot the points (-0.5, 0), (9.5, 5), (19.5, 14), (29.5, 30), (39.5, 52), (49.5, 78), (59.5, 96), (69.5, 107), (79.5, 113), (89.5, 117) and (99.5, 120).

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

(i) Median = $\dfrac{n}{2} = \dfrac{120}{2}$ = 60th term

Through P = 60, draw a horizontal line parallel to x-axis touching the ogive at point Q. From point Q draw a vertical line parallel to y-axis touching x-axis at R.

From graph,

R = 42.5

Hence, median = 42.5

(ii) Total marks = 100

75% of marks = 75

Through S = 75, draw a vertical line parallel to y-axis touching the ogive at point T. From point T draw a horizontal line parallel to x-axis touching y-axis at U.

From graph,

U = 111

∴ 111 students secured less than or equal to 75%

∴ 9 (120 - 111) students scored more than 75%.

Hence, 9 students scored more than 75% marks.