Histogram and Frequency Density

Definition:
Frequency density is defined as the ratio of the frequency of a class interval to the width of the class interval.

Formula:
Frequency Density = Frequency / Class Width

Use in Construction of Histogram:
Histogram is a graphical representation of a frequency distribution. It consists of a series of bars of equal width, drawn adjacent to each other. The area of each bar is proportional to the frequency of the class it represents. In case the class intervals are of unequal width, the height of each bar is not proportional to the frequency of the class it represents. Therefore, to make the height of each bar proportional to the frequency of the class it represents, we use frequency density instead of frequency.

Example:
Suppose we have a frequency distribution with the following class intervals and frequencies:

Class Interval | Frequency
---------------------------
0-10 | 4
10-20 | 10
20-30 | 14
30-40 | 8
40-50 | 2

We can calculate the frequency density by dividing the frequency of each class by its width:

Class Interval | Frequency | Width | Frequency Density
-------------------------------------------------------------
0-10 | 4 | 10 | 0.4
10-20 | 10 | 10 | 1.0
20-30 | 14 | 10 | 1.4
30-40 | 8 | 10 | 0.8
40-50 | 2 | 10 | 0.2

Using frequency density, we can construct a histogram where the height of each bar is proportional to the frequency density of the class it represents.