Find the modal height of the following distribution by drawing a histogram :
Find the modal height of the following distribution by drawing a histogram :
Height (in cm) 140-150 150-160 160-170 170-180 180-190
No. of students 7 6 4 10 2

Solution:

Construct histogram using given data.

Height (in cm) 140-150 150-160 160-170 170-180 180-190
No. of students 7 6 4 10 2

Represent height on X-axis and number of students on Y-axis.

Take scale: X axis : 2 cm = 10 (class interval)

Y axis : 1 cm = 1 (frequency)

In the highest rectangle, draw two straight lines AC and BD.

P is the point of intersection.

Draw a vertical line through P to meet the X-axis at M.

The abscissa of M is 174.

Hence the mode is 174.