Relative Frequency
Relative frequency is the proportion of times a value occurs in a dataset, expressed as a fraction or percentage of the total.
Formula
\text{Relative Frequency} = \dfrac{\text{frequency}}{\text{total number of values}}
Definition
Relative frequency is the fraction or percentage that tells you how often something happened compared to the total number of times you looked, the ratio of the frequency of a value or class to the total number of observations: relative frequency $= f_i/n$. Relative frequencies sum to $1$, can be expressed as percentages, and are directly comparable across datasets of different sizes. Formally, $f_i/n$ is the empirical probability of the i-th category, a nonparametric estimate of the underlying probability, and the empirical distribution function $F_n(x) = \frac{1}{n}\sum \mathbb{1}(X_i \le x)$ converges uniformly to the true CDF $F(x)$ by the Glivenko-Cantelli theorem.
Example
If you flip a coin $20$ times and get heads $12$ times, the relative frequency of heads is $12/20 = 0.6$, or $60\%$. In a class of $25$ students where $10$ prefer science, $8$ prefer math, and $7$ prefer English, the relative frequencies are science $= 10/25 = 0.40$, math $= 8/25 = 0.32$, and English $= 7/25 = 0.28$, summing to $1.00$. The Dvoretzky-Kiefer-Wolfowitz inequality gives $P(\sup|F_n(x)-F(x)| > \epsilon) \le 2e^{-2n\epsilon^2}$, providing a confidence band for the empirical CDF with explicit probability guarantees.
Key Insight
Relative frequency is useful when comparing groups of different sizes: saying "$60\%$ prefer option A" is more meaningful than "$30$ out of $50$ prefer it" when comparing to a group of $200$. It is the empirical estimate of probability, and by the law of large numbers it converges to the true probability as $n$ grows; this approach underpins bootstrap resampling, treating the empirical distribution as an approximation to the true distribution and resampling from it to estimate uncertainty.