Creating a frequency density histogram allows you to visualize the distribution of data, especially when dealing with unequal class widths. Here's how:
Understanding Frequency Density
Frequency density is crucial for histograms with varying class intervals. It solves the issue of unequal bar widths misrepresenting data. Instead of just showing frequency, frequency density accounts for the width of each class. It is calculated by dividing the frequency of a class by its class width.
- Formula: Frequency Density = Frequency / Class Width
Steps to Create a Frequency Density Histogram
- Organize your data: Arrange your data into classes (bins) with their respective frequencies.
- Calculate class widths: Determine the width of each class by subtracting the lower class boundary from the upper class boundary. Note that classes may have different widths.
- Calculate frequency densities: For each class, divide the frequency by its class width to find the frequency density.
- Draw the axes: Draw a horizontal axis (x-axis) representing the data values (class intervals) and a vertical axis (y-axis) representing the frequency density.
- Construct the bars: Draw a bar for each class with its base length matching the class width and its height corresponding to the calculated frequency density. The area of each bar represents the frequency.
Example
Let's say we have the following data:
| Class Interval | Frequency | Class Width | Frequency Density |
|---|---|---|---|
| 0-10 | 5 | 10 | 0.5 |
| 10-20 | 10 | 10 | 1 |
| 20-30 | 15 | 10 | 1.5 |
| 30-40 | 8 | 10 | 0.8 |
Following the steps above:
- We already have the data organized into classes and frequencies.
- Each class width is 10.
- Frequency densities are calculated (shown in the table above).
- The x-axis will show the class intervals (0-10, 10-20, 20-30, 30-40). The y-axis will show the frequency density (from 0 to 1.5).
- Bars will be drawn with heights according to frequency density and widths equal to class widths.
This histogram will accurately represent the distribution of the data even though the classes have equal widths. Remember: the area of the bar represents the frequency.
Resources for Further Learning
- YouTube Tutorials: Search YouTube for "frequency density histograms" for many visual guides. (e.g., Frequency density histograms - YouTube)
- Online Educational Resources: Websites like BBC Bitesize offer detailed explanations and examples. (e.g., Histograms - Representing data - Edexcel - GCSE Maths Revision)
