The relative frequency of a class in a histogram is computed by dividing the frequency of that class by the total number of observations in the dataset.
Here's a more detailed breakdown:
Understanding Relative Frequency
Relative frequency represents the proportion of times a particular class or category appears in a dataset. In the context of a histogram, each class represents a bin or interval of values.
Calculation Steps
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Determine the Frequency of Each Class (fi): Count the number of data points that fall within each specific class or bin. This count is the frequency of that class.
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Calculate the Total Number of Observations (n): Sum the frequencies of all classes. This is the total number of data points in the dataset.
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Compute the Relative Frequency: Divide the frequency of each class (fi) by the total number of observations (n). The formula is:
Relative Frequency = fi / n
Example
Imagine you have collected data on the ages of people visiting a library, and you've created a histogram with the following age classes:
| Age Class | Frequency (fi) |
|---|---|
| 0-10 | 25 |
| 11-20 | 40 |
| 21-30 | 30 |
| 31-40 | 15 |
| 41-50 | 10 |
The total number of observations (n) is 25 + 40 + 30 + 15 + 10 = 120.
To calculate the relative frequency for the 0-10 age class:
Relative Frequency = 25 / 120 = 0.2083 (approximately 20.83%)
This means that approximately 20.83% of the library visitors are between 0 and 10 years old.
Significance
The relative frequency provides a standardized way to compare the frequency of different classes, regardless of the total sample size. It's particularly useful when comparing datasets with different numbers of observations. Relative frequencies are often expressed as percentages. Histograms often display relative frequency on the y-axis instead of absolute frequency, allowing for easy comparison of distributions with different sample sizes.
