Class density, also known as frequency density, is found by dividing the frequency of a class by its width. This calculation is essential when dealing with grouped data that has unequal class intervals, as it allows for a fair comparison of the concentration of data within each class.
Here's a breakdown of the process:
1. Understand the Need for Class Density
When you have grouped data where the class intervals (widths) are not the same, simply comparing the frequencies can be misleading. A wider class interval might naturally have a higher frequency simply because it covers more values. Class density corrects for this.
2. Define the Terms
- Frequency: The number of observations within a specific class interval.
- Class Width: The difference between the upper and lower boundaries of a class interval. For example, if a class interval is 10-20, the class width is 20 - 10 = 10.
3. The Formula
The formula for class density is:
Class Density = Frequency / Class Width4. Step-by-Step Calculation
a. Determine the frequency for each class interval.
b. Calculate the class width for each class interval.
c. Divide the frequency by the class width for each class interval. The result is the class density for that interval.
5. Example
Let's say you have the following data:
| Class Interval | Frequency |
|---|---|
| 0-10 | 5 |
| 10-15 | 8 |
| 15-30 | 12 |
Calculations:
- Class 1 (0-10):
- Frequency = 5
- Class Width = 10 - 0 = 10
- Class Density = 5 / 10 = 0.5
- Class 2 (10-15):
- Frequency = 8
- Class Width = 15 - 10 = 5
- Class Density = 8 / 5 = 1.6
- Class 3 (15-30):
- Frequency = 12
- Class Width = 30 - 15 = 15
- Class Density = 12 / 15 = 0.8
6. Interpretation
In the example above, the class interval 10-15 has the highest class density (1.6), indicating that the data is most concentrated within that range, even though the class interval 15-30 has a higher frequency.
7. Using Class Density for Visualization
Class density is frequently used to construct histograms when class intervals are unequal. In this case, the y-axis of the histogram represents the density, not the frequency, ensuring that the area of each bar is proportional to the frequency.
In summary, class density is a normalized measure that allows for meaningful comparisons of data distribution across classes with different widths. It's calculated by dividing the frequency by the class width and is particularly useful for histograms with unequal class intervals.
