You can't directly find density from just relative frequency. You need additional information, specifically the class width (or bin width) of the data. Density, in this context, refers to frequency density, which is a crucial concept in histograms. It represents the frequency per unit of the x-axis.
Understanding the Relationship
Relative frequency shows the proportion of data falling within a specific range (class or bin). To obtain frequency density, you must consider how this relative frequency is distributed across the width of that range.
- Relative Frequency: The proportion of data in a specific bin. Calculated as (frequency of the bin) / (total frequency).
- Frequency Density: The frequency per unit of the x-axis (class width). Calculated as (frequency of the bin) / (width of the bin).
- Class Width (Bin Width): The range of values encompassed by a single bin in a histogram.
Calculating Frequency Density from Relative Frequency
To calculate the frequency density, follow these steps:
- Determine the Relative Frequency: Calculate the relative frequency for the bin of interest.
- Find the Class Width: Determine the width of the bin. This is the difference between the upper and lower boundaries of the bin.
- Calculate the Frequency Density: Multiply the relative frequency by the total frequency, and then divide by the class width. This is equivalent to: (Frequency of the bin) / (width of the bin).
Example:
Let's say you have a bin with a relative frequency of 0.2 (20%) and a width of 5 units. If your total frequency (number of data points) is 100, the frequency density would be:
(0.2 * 100) / 5 = 4
This means that there are 4 data points per unit of the x-axis within that specific bin.
Note: As shown in the provided text, some sources define relative frequency density as frequency density divided by the total frequency. This is consistent with the calculation outlined above, showing the relationship between the various terms.
Important Considerations:
- Histograms: Frequency density is particularly important when dealing with histograms where the bin widths are unequal. It allows for a fair comparison between bins of different sizes.
- Probability Density Functions: In probability, the concept extends to probability density functions, where the area under the curve represents the probability rather than the absolute frequency. A relative frequency histogram can be used as an approximation to a probability density function.
