Table of Contents
What Is Relative Frequency?
Relative frequency is the ratio of the number of times a particular event occurs to the total number of trials or observations. It is an empirical (experimental) estimate of probability. As the number of trials increases, the relative frequency of an event tends to converge to the theoretical probability of that event (this is the Law of Large Numbers).
Relative frequency is fundamental in descriptive statistics for constructing frequency distributions, histograms, and pie charts. It allows you to compare categories of different sizes and is the basis for the frequentist interpretation of probability.
Formula
Percentage = (f / n) × 100%
Cumulative Relative Frequency = sum of all relative frequencies up to a class
Where f is the frequency (count) of the event and n is the total number of observations. All relative frequencies in a distribution must sum to 1 (or 100%).
Example: Survey Results
| Response | Frequency | Relative Frequency | Percentage |
|---|---|---|---|
| Strongly Agree | 30 | 0.30 | 30% |
| Agree | 40 | 0.40 | 40% |
| Neutral | 15 | 0.15 | 15% |
| Disagree | 10 | 0.10 | 10% |
| Strongly Disagree | 5 | 0.05 | 5% |
| Total | 100 | 1.00 | 100% |
Frequently Asked Questions
What is the difference between frequency and relative frequency?
Frequency is the raw count of how many times an event occurs. Relative frequency is that count divided by the total number of observations, giving a proportion between 0 and 1. Relative frequency allows meaningful comparisons between datasets of different sizes.
How does relative frequency relate to probability?
Relative frequency provides an empirical estimate of probability. According to the Law of Large Numbers, as the number of trials approaches infinity, the relative frequency of an event converges to its true theoretical probability. This is the foundation of the frequentist approach to probability.