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. Let us learn about the relative frequency formula with few solved examples.
What Is the Relative Frequency Formula?
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
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 frequencies
Solved Examples Using Relative Frequency Formula
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, number of times a die is tossed = 30
Number of the successful trials of getting number 6 = 5
By the formula, we know,
Relative frequency = Number of positive trial / Total number of trials
f = 5/ 30 = 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 favorites 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.
| Candy color | Yellow | Red | Green | Brown |
|---|---|---|---|---|
| Frequency | 6 | 6 | 3 | 5 |
A) What is the relative frequency of the picked candy being one of her favorites?
B) What is the relative frequency for 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 favorites:
(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, 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%.
FAQs on Relative Frequency Formula
What Is Relative Frequency Formula?
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. The relative frequency formula is given as: Relative Frequency = Subgroup frequency/ Total frequency.
What's the Difference Between Frequency and Relative Frequency?
An easy way to define the difference between frequency and relative frequency is that frequency relies on the actual values of each class in a statistical data set while relative frequency compares these individual values to the overall totals of all classes concerned in a data set.
Is Relative Frequency and Probability the Same?
A relative frequency is found on the basis of the experimental probability. The probability is a number between 0 and 1.0 indicating the likelihood of an event. This defines probability as the number of times an event occurs divided by the number of opportunities for it to occur. The result of this calculation is called the “relative frequency” of the event.
Is Relative Frequency a Percentage?
A relative frequency count is a measure of the number of times that an event occurs out of the total events. It can be expressed as a proportion. It is also often expressed as a percentage
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