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Relative Frequency Formula

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  • Last Updated : 01 May, 2022

Frequency in mathematics is a measure of how often a quantity is present and represents the chances of occurrence of that quantity. In other words, frequency depicts how many times a particular quantity has occurred.

What is Relative Frequency?

  • Relative frequency is an extension of frequency where each frequency is represented relative to all the present frequencies of different quantities. 
  • Frequency in mathematics represents the actual occurrence of quantities whereas relative frequency represents the occurrence of quantities relative to each other.

Formula of Relative Frequency 

The formula for relative frequencies are:

Relative frequency of a given number (x) = Frequency of the given number(x) / Sum of frequency of all given quantities (x, x1, x2, x3, x4, x5, x6…….xn)

or

Relative Frequency = Frequency of that class or value / Total size of the data set

or 

Relative frequency = Subgroup count / Total count

Sample Questions

Question 1: Vaibhav has 5 oranges, 10 mangoes, and 6 bananas. Find the relative frequency of each fruit.

Answer: 

Given the Frequency of oranges = 5

Frequency of mangoes = 10

Frequency of bananas = 6

Sum of frequency of all the fruits = Frequency of oranges + Frequency of mangoes + Frequency of bananas

= 5 + 10 + 6

=21

Relative Frequency of oranges = Frequency of oranges/ Sum of frequency of all the fruits 

= 5/21

Relative Frequency of mangoes = Frequency of mangoes/ Sum of frequency of all the fruits 

= 10/21

Relative Frequency of bananas = Frequency of bananas/ Sum of frequency of all the fruits 

= 6/21

Question 2: A class has 55 boys and 35 girls. Find the relative frequency of each gender.

Answer: 

Given the Frequency of boys = 55

Frequency of girls = 35

Sum of frequency of both genders = Frequency of boys + Frequency of girls

= 55 + 35

= 90

Relative Frequency of boys = Frequency of boys/ Sum of frequency of both genders 

= 55/90

Relative Frequency of girls = Frequency of girls/ Sum of frequency of both genders 

= 35/90

Question 3: Anu has 6 candies, 8 chocolates, 4 toffees, and 8 lollipops. Find the relative frequency of each.

Answer: 

Given Frequency of candies = 6

Frequency of chocolates = 8

Frequency of toffees = 4

Frequency of lollipops = 8

Sum of frequency = Frequency of candies + Frequency of chocolates + Frequency of toffees + lollipops

= 6 + 8 + 4 + 8

= 26

Relative Frequency of candies = Frequency of candies/ Sum of frequency 

= 6/26

Relative Frequency of chocolates = Frequency of chocolates/ Sum of frequency 

= 8/26

Relative Frequency of toffees = Frequency of toffees/ Sum of frequency 

= 4/26

Relative Frequency of lollipops = Frequency of lollipops/ Sum of frequency 

= 8/26

Question 4: A player has 7 gold medals, 4 silver medals, and 9 bronze medals. Find the relative frequency of each medal.

Answer:

Given the Frequency of gold medals = 7

Frequency of silver medals = 4

Frequency of bronze medals = 9

Sum of frequency of all the medals = Frequency of gold medals + Frequency of silver medals + Frequency of bronze medals

= 7 + 4 + 9

= 20

Relative Frequency of gold medals = Frequency of gold medals/ Sum of frequency of all the medals

= 7/20

Relative Frequency of silver medals = Frequency of silver medals/ Sum of frequency of all the medals

= 4/20

Relative Frequency of bronze medals = Frequency of bronze medals/ Sum of frequency of all the medals

= 9/20

Question 5: A class has 5 boys scoring 100 marks and 4 girls scoring 100 marks. Find the relative frequency of each gender that has scored 100 marks.

Answer: 

Given the Frequency of boys scoring 100 marks= 5

Frequency of girls scoring 100 marks= 4

Sum of frequency of both genders scoring 100 marks

= Frequency of boys scoring 100 marks + Frequency of girls scoring 100 marks

= 5 + 4

= 9

Relative Frequency of boys scoring 100 marks = Frequency of boys scoring 100 marks/ Sum of frequency of both genders scoring 100 marks 

= 5/9

Relative Frequency of girls scoring 100 marks = Frequency of girls scoring 100 marks/ Sum of frequency of both genders scoring 100 marks

= 4/9

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