Draw a histogram for the following distribution :

Marks out of 80	No. of students
40-44	2
45-49	8
50-54	12
55-59	10
60-64	8

Hence, estimate the mode.

By formula,

Adjustment factor =

$\dfrac{\text{Lower limit of a class - Upper limit of preceding class}}{2} = \dfrac{45 - 44}{2} = \dfrac{1}{2}$ = 0.5

New lower class limit = Lower class limit - Adjustment factor

New upper class limit = Upper class limit + Adjustment factor

Steps of construction :

1. Draw a histogram of the given distribution.

2. Inside the highest rectangle, which represents the maximum frequency (or modal class), draw two lines AC and BD diagonally from the upper corners C and D of adjacent rectangles.

3. Through the point E (the point of intersection of diagonals AC and BD), draw EF perpendicular to the horizontal axis.

4. The value of point F on the horizontal axis represents the value of mode.

From graph,

F = 52.75

Hence, required mode = 52.75.