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.