# Relative Frequency

A frequency is the number that tells how many times a data or an event is repeating in an experiment. It is generally represented graphically in form of histograms.

There are two different types of frequencies:

1) Cumulative Frequency:  It is the total of all the absolute frequencies of all the events that are below of at the particular point in a given list of events that is formulated in an order.

2) Relative Frequency: It refers to the absolute frequency of an event that is normalized by the total number of the given events.
Relative frequency is used in probability when it is not easy to evaluate the probability of certain events by looking at their situations. For example the result of any match for win, lose or tie cannot be determined as all outcomes are equally likely, but one can estimate the probability by looking at the previous win or lose of matches and also the way the game is proceeding so far.

## Formula

The relative frequency can be evaluated by suing the following formula:

Relative frequency = $\frac{(number\ of\ trials\ that\ are\ successful)}{(total\ number\ of\ trials )}$

With increase in number of trials the estimate of the probability that is made using the relative frequency technique can be more accurate.
Relative frequency tells how often anything is happening after dividing by the total number of outcomes. It is more an experimental concept than a theoretical one. In general we use the relative frequency concept in case of big number of trials. This can only be done practically and not theoretically. Since the concept is experimental so it is quite possible to get distinct relative frequency each time the experiment is repeated.

For Example: I have scored an ‘A’ 7 times out of the 10 tests. Then 7 is my frequency of scoring an ‘A’ and $\frac{7}{10}$ * 100% = 70% is the relative frequency of my scoring an ‘A’ in exams.

When we add up all the relative frequencies, the sum is equal to 1 always, neglecting the rounding off if any.

## Problems

Below are some examples on relative frequency.

Example 1: 12 cards are numbered distinctly from 1 to 12 without repetition. One card is drawn at a time and the number is recorded and then the card is placed back. This is done 50 times and following outcomes were recorded.

 4 10 6 12 5 10 5 6 12 11 1 6 3 1 6 1 2 1 5 4 4 12 6 6 1 12 4 10 12 3 8 6 12 9 8 4 3 8 12 3 12 5 4 11 12 5 5 5 8 5 12

Find the probability of occurrence of 12.

Solution:

Here we see that occurrence of 12 is 11 times in all 50 trials.

So in this case the probability of occurrence of 12 is simply the relative frequency of 12.

P (occurrence of 12) = $\frac{11}{50}$ = 0.22

Relative frequency = 0.22 = 22%

So in an experiment of 50 trials 12 has occurred 22%.

Example 2: In a class of 42 students, 20 students go to school by school bus, 15 by car and 7 by walk. Find the relative frequencies.

Solution: Total number of students = 42

Number of students used school bus = 20

Number of students used car = 15

Number of students go by walk = 7

The relative frequencies are:

School bus = $\frac{20}{42}$ = 0.48

Car = $\frac{15}{42}$ = 0.36

Walk = $\frac{7}{42}$ = 0.17