4.6.1 Frequency Density

Frequency density is a statistical concept that describes the density of frequency distribution in a given range of values. 

• It is calculated by dividing the frequency of a particular class by the width of that class.

• Frequency density represents the concentration of data points in a specific range or class interval. 

• It is often used to create histograms or frequency polygons, which are graphical representations of frequency distributions.

• The formula for frequency density is:

\( Frequency \ Density = \frac {Frequency \ of \ Class}{Width \ of \ Class \ Interval} \)

• Where

  • Frequency of a class refers to the number of data points in that particular class

  • Width of the class interval is the difference between the upper and lower limits of that class

• To calculate frequency density

  • Determine the frequency of a particular class

    • Count the number of data points that fall within the class interval

  • Determine the width of the class interval

    • Subtract the lower limit of the class from the upper limit

  • Divide the frequency by the width of the class interval

    • This gives you the frequency density for that class

  • Repeat this process for all classes in your data set.

Worked example:

Suppose you have the following data set, which represents the ages 

of a group of people.

To calculate the frequency density for the first class \( (20 \) – \( 24 \) )

Find frequency of Class

Which is\( 10 \)

Width of Class Interval

Which is\( 4 \)

Now use the formula

\( Frequency \ Density = \frac{Frequency \ of \ Class}{Width \ of \ Class \ Interval} \)

\( Frequency \ Density = \frac{10}{4}=2.5 \)

Therefore, the frequency density for the \( 20 \) – \( 24 \) age group is \( 2.5 \).

Repeat this process for all other classes to get the frequency density for each class.

The frequency density for the \( 25 \) – \( 29 \) age group will be

\( \frac{15}{4}=3.75 \)

The frequency density for the \( 30 \) – \( 34 \) age group will be

\( \frac{12}{4}=3 \)

The frequency density for the \( 35 \) – \( 39 \) age group will be

\( \frac{8}{4} = 2 \)