Relative Frequencies and Cumulative Relative Frequencies

There are several types of frequencies that provide different insights into your data:

• Absolute Frequency: This is the simple count of observations in each category. In our example above, we can see that 6 observations fall into the interval 4 <= r < 6, representing the highest count in any single interval.
• Relative Frequency: Relative frequency shows the proportion of observations in each category compared to the total observations. It's calculated by dividing the absolute frequency by the total number of observations. Relative frequencies are often expressed as percentages and always sum to 100%.
• Cumulative Relative Frequency: This measure is particularly useful for understanding the distribution of data up to a certain point. It answers questions like "What percentage of observations fall below a certain value?" For instance, from our table below, we can see that 70% of all observations fall below 6.

The data in a frequency distribution can also be presented using relative frequencies.

Once we have relative frequencies, we can calculate cumulative relative frequencies where as we move from first frequency interval to the last, we keep adding the relative frequencies finally reaching 100%. Cumulative relative frequencies are useful in measuring what fraction of total observations are less than the upper limit of a frequency interval.

We will extend our example to show the relative frequencies and cumulative relative frequencies.

The cumulative relative frequency is equal to the some of the relative frequencies of all the previous intervals including the current interval. For example, the cumulative absolute frequency for the interval 4 <= r < 6 is 15% + 25% + 30% = 70%.