Frequency refers to the total number of observations of a determined type. Based on the given problem frequency of a value can be expressed in different ways. In a simplest way frequency can be expressed in its absolute terms. Absolute frequency refers to the number of times a particular value for a variable has been observed to occur.

Relative frequency is also calculated by dividing the absolute frequency by the total number.

To find relative frequency we divide the number of observations of a certain type with its total. All the relative frequencies add up to 1.

It is also known as empirical probability. It is how often something happens over all the outcomes.

For Example : When a coin is flipped 8 times and you get tails 3 times then the relative frequency will be 3 over 8.

## Definition

Relative frequency of an event refers to the absolute frequency normalized by the total number of events.

$f_{i}$  = $\frac{n_{i}}{\sum_{i}n_{i}}$

It is evaluated by dividing the individual frequency of an item by total number of frequencies. It can be expressed as a percentage and is denoted by $f_{i}$.

Example : If s group of students eat 4 candies out of 13 candies then
The frequency of eating candies is 4.

Relative frequency of eating candies is $\frac{4}{13}$ = 0.31.

## Formula

Relative frequency of an outcome is found using the below formula.
Relative frequency = $\frac{Number\ of\ successful\ trials}{Total\ number\ of\ trials}$Once the relative frequency is known it is easier to estimate the probability of a particular outcome.

If there are more trials then the probability estimate will be more accurate.

## Approach

In three simple steps the relative frequency approach is explained below:
1) Firstly observe an event happening for a large number of times. (Total number of matches played)
2) Next step is to have a count on the number of times the event occurs. (Number of matches won)
3) Final step is to estimate the probability of event by calculating the proportion of times the event occurred. (Matches won/ Total number of matches played)

## Graph

Relative Frequency graph is more useful than a comparison of absolute frequencies. Relative frequency graph represents a bar graph. The data considered is of categorical type and we compare different frequencies. The height of the bars shows the relative frequency for each category.

The concept is clearly explained with example:

For the following data construct the relative frequency table and plot the graph.
5, 3, 2, 8, 9, 5, 4

Solution : Number of observations  = 7

Formula for relative frequency is $\frac{Number\ of\ successful\ trials}{Total\ number\ of\ trials}$

Given below is the relative frequency table:
 x Frequency  ($n_{i}$) Relative Frequency = $\frac{n_{i}}{\sum_{i}n_{i}}$ 1 5 $\frac{5}{38}$ = 0.13 2 3 $\frac{3}{38}$ = 0.08 3 2 $\frac{2}{38}$ = 0.05 4 8 $\frac{8}{38}$ = 0.21 5 9 $\frac{9}{38}$ = 0.24 6 7 $\frac{7}{38}$ = 0.18 7 4 $\frac{4}{38}$ = 0.10 $\sum_{i} n_{i}$ = 38

## Table

Relative frequency table helps in organizing information on how something happened in a tabular form. It clearly presents the total count for each category. Lets study this concept more clearly with the help of examples.

Example : Construct the relative frequency table for the below data.
 Class Interval Frequency 0 - 5 5 5 - 10 1 10 - 15 6 15 - 20 8 20 - 25 5

Solution :
Formula for relative frequency is $\frac{Number\ of\ successful\ trials}{Total\ number\ of\ trials}$

The table of relative frequency is given below:
 Class Interval Frequency (n$_{i}$) Relative Frequency = $\frac{n_{i}}{\sum_{i}n_{i}}$ 0  -  5 5 $\frac{5}{25}$ = 0.2 5  -  10 1 $\frac{1}{25}$ = 0.04 10  -  15 6 $\frac{6}{25}$ = 0.24 15  -  20 8 $\frac{8}{25}$ = 0.32 20  -  25 5 $\frac{5}{25}$ = 0.2 $\sum_{i} n_{i}$= 25

Example 2 : Find the relative frequencies for the following frequency distribution.

 Weekly wages (less than '00 Rs) 15 36 66 17 26 39 Number of workers 12 2 15 8 13 22

Solution : Total number of workers = 72
The table of relative frequency is given below
 Weekly wages (less than '00 Rs) Number of workers (n$_{i}$) Relative Frequency = $\frac{n_{i}}{\sum_{i}n_{i}}$ 15 12 $\frac{12}{72}$ = 0.17 36 2 $\frac{2}{72}$ = 0.03 66 15 $\frac{15}{72}$ = 0.21 17 8 $\frac{8}{72}$ = 0.11 26 13 $\frac{13}{72}$ = 0.18 39 22 $\frac{22}{72}$ = 0.31 $\sum_{i} n_{i}$ = 72