Relative Frequency Formula

The word 'relative' is used to indicate that an event is being considered in relation or in proportion to something else. Frequency is a way to measure how often a particular event occurs. Relative frequency, on the other hand, is a way to measure how often a particular event occurs against total occurrences.

The relative frequency formula says: relative frequency = f/n, where 'f' is the frequency of a specific group and 'n' is the total frequency. Let us learn about the relative frequency formula with a few solved examples.

What is the Relative Frequency Formula?

The relative frequency formula is a statistical tool that is used to calculate the proportion of the occurrence of an event in a sample or population. Relative frequency can be defined as the number of times an event occurs divided by the total number of events occurring in a given scenario.

To calculate the relative frequency two things must be known:

• Number of total events/trials
• Frequency count for a category/subgroup

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Relative Frequency Formula

The relative frequency formula can be given as:

Relative Frequency = Subgroup frequency/ Total frequency

Or

Relative Frequency = f / n

where,

• f is the number of times the data occurred in an observation
• n = total frequency

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Relative Frequency Formula Examples

Example 1: A cubical die is tossed 30 times and lands 5 times on the number 6. What is the relative frequency of observing the die land on the number 6?

Solution: Given, the number of times a die is tossed = 30

Number of successful trials of getting the number 6 = 5

By the formula, we know,

Relative frequency = Number of positive trials / Total number of trials

f = 5/ 30 = 1/6 (or) 16.66%

Answer: The relative frequency of observing the die land on the number 6 is 16.66%

Example 2: Anna has a packet containing 20 candies. Her favourites are the yellow ones and the red ones. The table below shows the frequency of each different candy selected as she picked all 20 sweets one by one and finished them all.

A) Find relative frequency of the picked candy being one of her favourites?

B) Find relative frequency of the brown candy

Solution: Relative frequency = number of times an event has occurred / number of trials

A) Relative frequency of the picked candy to be one of her favourites:

(Frequency of yellow + Frequency of red candy)/ 20 = 12/ 20 = 60%

B) Relative frequency of the brown candy

Frequency of brown candy/ 20 = 5 / 20 = 25%

Answer: 60% and 25%

Example 3: A coin is flipped 100 times, and the coin lands on heads 48 times. What is the relative frequency of the coin landing on tails?

Solution: Relative frequency = number of times an event has occurred / number of trials

The event in consideration is the coin landing on tails = 100 - 48 = 52 times

Relative frequency of the coin landing on tails = 52/100 = 0.52 = 52%

Answer: Relative frequency of the coin landing on tails is 52%.