Find the mode of the following distribution by drawing a histogram :

C.I.	Frequency
1-6	6
7-12	12
13-18	20
19-24	15
25-30	9

Adjustment factor

$= \dfrac{\text{Lower limit of a class - Upper limit of preceding class}}{2} \\[1em] = \dfrac{7 - 6}{2} = \dfrac{1}{2} \\[1em] = 0.5$

New lower limit = Lower limit - Adjustment factor

New upper limit = Upper limit + Adjustment factor

Steps :

1. Take 2 cm along x-axis = 6 units and 1 cm along y-axis = 3 units.

2. Since, the scale on x-axis starts at 0.5, a break (zig-zag curve) is shown near the origin along x-axis to indicate that the graph is drawn to scale beginning at 0.5 and not at origin itself.

3. Construct rectangles corresponding to the given data.

4. In highest rectangle, draw two st. lines AC and BD from corners of the rectangles on either side of the highest rectangle to the opposite corners of the highest rectangle. Let P be the point of intersection of AC and BD.

5. Through P, draw a vertical line to meet the x-axis at M. The abscissa of the point M represents 16.

Hence, mode = 16.