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.
| Candy colour | Yellow | Red | Green | Brown |
|---|---|---|---|---|
| Frequency | 6 | 6 | 3 | 5 |
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%.
FAQs on Relative Frequency Formula
What Does Relative Frequency Formula State?
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.
What is Relative Frequency Distribution?
A relative frequency distribution is a statistical representation that shows the proportion/percentage of observations of different categories/intervals in a given dataset. It is useful to summarize data and identify the patterns.
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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