# Relative Frequency

The term relative frequency is used for the ratio of the observed frequency of an outcome and the total frequency of the random experiment. Suppose a random experiment is repeated $N$ times and an outcome is observed $f$ times. In this case, the ratio $\frac{f}{N}$ is called the relative frequency of the outcome which has been observed $f$ times. Some examples of relative frequencies are:

• We select bulbs from a certain big lot to examine whether they are good or defective. We take $100$ such bulbs and examine them. Sixty bulbs are found to be defective. The symbol $N$ may be used for $100$ and the symbol $f$ may be used for the observed frequency, which is $60$. Thus the ${\text{Relative frequency}} = \frac{f}{N} = \frac{{60}}{{100}} = 0.6$
• We are interested in knowing whether a coin is unbiased (true) or not. We toss the coin $200$ times and note the number of heads. In $200$ tosses, the number of heads is $110$. The relative frequency of this experiment for the number of heads is $\frac{{110}}{{200}}$, which is not $\frac{1}{2}$. As we shall see later, the probability of heads is usually written as $\frac{1}{2}$. It is just an assumption and, of course, a big assumption. If we repeat the same experiment again, the number of heads may be less than or more than $110$ as was observed in the first experiment. This is what happens in random experiments.
• A die is thrown and we are interested in the ace (face 1). We throw the die $60$ times and the ace is observed $12$ times. Thus the relative frequency of the ace is $\frac{{12}}{{60}} = \frac{1}{5}$. For an ideal die one should expect that the number of aces would be $\frac{{60}}{6} = 10$. At some later stage we would like to know more about the ratio $\frac{{12}}{{60}}$. This ratio is not constant. The next random experiment with the same die may produce a completely different result.