Relative Frequency Formula:
The term 'relative' denotes the consideration of an event concerning or in proportion to something else. Frequency quantifies the occurrence rate of a particular event. Relative frequency, however, measure the occurrence rate of a specific event in comparison to the total occurrences.
The formula for relative frequency is defined as: relative frequency = f/n, where 'f' represents the frequency of a particular group, and 'n' stands for the total frequency. Exploring the relative frequency formula through solved examples can provide a clearer understanding.
What is Relative Frequency Formula
The relative frequency formula serves as a statistical method for determining the proportion of event occurrences within a sample or population. Relative frequency is characterized by the event's occurrence count divided by the total count of events within a particular context.
To compute the relative frequency, it's essential to have two key pieces of information:
The total count of events or trials.
The frequency count for a specific category or subgroup.
Relative Frequency Formula
Expressed as:
Relative Frequency = Frequency of Subgroup / Total Frequency
Alternatively,
Relative Frequency = f / n
where,
f represents the occurrences of the data within an observation
n signifies the total frequency
Relative Frequency Formula Solved Example
Example 1:
When a cubical die is thrown 30 times, and it lands 5 times on number 6. What is the relative frequency of observing the die landing on the number 6?
Solution: With the given number of die tosses = 30
Occurrences of landing on number 6 = 5
Utilizing the formula:
Relative frequency = Number of specific occurrences / 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:
Consider a survey of 80 people in which 20 individuals prefer tea. What is the relative frequency of people who favor tea in this survey?
Solution:
Total surveyed individuals = 80
Individuals who prefer tea = 20
Using the formula:
Relative frequency = Individuals who prefer tea / Total surveyed individuals
Therefore, f = 20/80 = 1/4 (or) 25%
Answer: The relative frequency of people favoring tea in the survey is 25%.
Example 3:
In a deck of cards, a heart card appears 13 times out of 52 cards. What is the relative frequency of drawing a heart card from the deck?
Solution:
Total cards in the deck = 52
Heart cards = 13
By using the formula:
Relative frequency = Heart cards / Total cards in the deck
Hence, f = 13/52 = 1/4 (or) 25%
Answer: The relative frequency of drawing a heart card from the deck is 25%.
Example 4:
An experiment involving flipping a coin results in 30 occurrences of landing on heads out of 50 flips. What is the relative frequency of getting heads?
Solution:
Total coin flips = 50
Occurrences of landing on heads = 30
Utilizing the formula:
Relative frequency = Occurrences of heads / Total coin flips
Therefore, f = 30/50 = 3/5 (or) 60%
Answer: The relative frequency of getting heads from the coin flips is 60%.
The concept of relative frequency is pivotal in statistical analysis. It provides a means to quantify the occurrence of specific events within a broader context, offering insights into the distribution and likelihood of outcomes.
By utilizing the relative frequency formula, which calculates the ratio of occurrences of a particular event to the total number of observations, we gain a clearer understanding of how frequently these events happen relative to the entire set.
Through various examples, such as die rolls, card draws, or survey results, we've demonstrated the practical use of the relative frequency formula in different scenarios. This tool allows us to determine the proportion of specific occurrences within a sample or population, aiding in decision-making and understanding probabilities.
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