Relative Frequency

The term relative frequency is used for the ratio of the observed frequency of some outcome and the total frequency of the random experiment. Suppose a random experiment is repeated N times and some outcomes is observed f times, then 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 given here:

    • We select bulbs from a certain big lot to examine whether they are good or defective. We take, say 100 such bulbs and examine them. Sixty bulbs are found 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 to know whether a coin is unbiased (true) or not. We toss the coin say 200 times and note that the number of heads. In 200 tosses, the number of heads may be, say110. The relative frequency of this experiment for number of heads is \frac{{110}}{{200}} which is not \frac{1}{2}. As we shall see later, the probability of head is usually written as \frac{1}{2}. It is just as assumption and of course a big assumption. If we repeat the same experiment again, the number of heads may be less than or more than110 as 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 say 60 times and ace is observed12 times. Thus the relative frequency of aces 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 something constant. A next random experiment with the same die may produce a completely different results.   



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