# Relative Frequency

Relative frequency is the ratio between the observed frequency of an outcome and the total frequency of any random experiment.

Relative frequencies will not be equal, if number of relative frequencies are evaluated from the same experiment. But it should also be remember that their sum is always equal to one.

## Relative frequency formula:

Let consider a randomly carried out experiment is repeated N times and the total number of outcomes that are observed are f times.

N = number of times a random experiment is repeated

f = number of times an outcome is observed

Then, relative frequency = f/N

## Relative Frequency Examples:

Here are the few examples that will explain the importance of relative frequency in probability problems.

### Example 1:

To check either the company is manufacturing good or defective bulbs. 150 bulbs are selected randomly from a certain big lot for the examination. After the examination it is found 80 bulbs out of 150 are defective. Find the relative frequency.

Solution:

Let N = total number of selected bulbs = 150

f = observed frequency = 80

Relative frequency = f/ N = 80/150 = 0.53

### Example 2:

A die is rolled 60 times on the table and at that time our interest was to appear (face 5). During experiment face 5 appears 20 times out of 60. Find the relative frequency.

Solution:

Let N = number of times a die is rolled = 60

f = number of times face 5 is observed during experiment = 20

Relative frequency will be;

Relative frequency = f/N = 20/60 = 0.33

### Example 3:

A fair coin is tossed 200 times. During toss, our interest was the number of times a head appears. It is observed that 120 times head appears out of 200. Find the relative frequency of the experiment.

Solution:

Let N = number of times a coin is tossed

f = number of times head appears

Relative frequency = f/N = 120/200 = 0.6 ≠ ½

This example is not only for relative frequency, but it also clears that during random experiment we mostly took the probability of head ½. This is only an assumption for creating sample space, because sample space can only be created for discrete variables not for the continuous variables.