Frequency Density

 

What Is Frequency Density?

When drawing histograms, especially with grouped data that has unequal class widths, we use frequency density to ensure the bars represent data fairly.

Frequency Density Formula:

$$\text{Frequency Density} = \frac{\text{Frequency}}{\text{Class Width}}$$

• Class width is the difference between the upper and lower boundary of the interval.
• Frequency density tells us how “dense” the data is in each interval.

 

Why Do We Use Frequency Density?

• If all class widths are equal, the height of the bar can represent frequency directly.
• If class widths are unequal, just using the height can be misleading.
• Using frequency density ensures the area of each bar (not height) shows the correct frequency.

 

How Do I Calculate Frequency Density?

Step-by-step:

1. Find class widths for each interval:
   • Subtract the lower value from the upper value in each class.
2. Apply the formula for each row:
   • Divide the frequency by the class width.

 

Example

The table below shows the number of deliveries completed in a courier network by delivery time.

 

Delivery Time (minutes)	Frequency
$10 \leq t < 30$	4
$30 \leq t < 40$	10
$40 \leq t < 45$	18
$45 \leq t < 50$	26
$50 \leq t < 60$	12

 

Let’s add two extra columns: class width and frequency density

 

Delivery Time (min)	Frequency	Class Width	Frequency Density
$10 \leq t < 30$	4	20	$\frac{4}{20} = 0.2$
$30 \leq t < 40$	10	10	$\frac{10}{10} = 1$
$40 \leq t < 45$	18	5	$\frac{18}{5} = 3.6$
$45 \leq t < 50$	26	5	$\frac{26}{5} = 5.2$
$50 \leq t < 60$	12	10	$\frac{12}{10} = 1.2$