104 LearnersLast updated on June 12th, 2025
How To Find Relative Frequency
In math, frequency is how often a value appears in a dataset. Relative frequency refers to the ratio of an event's occurrences to the total number of observations. Relative frequency is an important concept and can be useful while working with probability, statistics, scientific experiments, and market research. Let us learn more about relative frequency in this article.
How to Find Relative Frequency?
Relative frequency is defined as the ratio between the total number of times an event occurs and the number of events in the dataset. It is often expressed as a percentage, fraction, or decimal. Calculating relative frequency helps to analyze distributions, choose data-driven choices, and predict future results. To find the relative frequency, we need two key values:
- The total number of events or trials
- The frequency of a specific event
Imagine 40 students taking a test, with 10 of them scoring an A. Now, calculating the relative frequency of students scoring an A will help analyze the proportion of high-performing students. However, in order to find the relative frequency, we must first find the frequency of the term by analyzing the provided data. Once this is done, we can then find the total frequency of all terms in the dataset. The last step is to divide the frequency of a single term by the total frequencies to get the relative frequency.
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Formula to Find Relative Frequency
To find the relative frequency of any given statistical data, we can use the relative frequency formula. The general formula of relative frequency is:
Relative frequency = f / n, where f is the frequency and n is the number of data values given.
This formula helps compare the occurrences to the total number of events in a dataset. Now, we can consider an example with the formula of relative frequency. Let's say a class has 40 students out of which 10 scored A in an exam. Here, we need to find the relative frequency of those who scored A. The formula is:
Relative frequency = f / n
Relative frequency = 10 / 40 = 0.25
Now, we need to convert 0.25 to percentage by multiplying it with 100.
So, 0.25 × 100 = 25%
This means that 25% of the class scored a minimum of A in the exam.
Importance of Finding Relative Frequency for Students
Understanding how relative frequency works will help us ascertain the frequency of an event compared to the number of events. Students can use this data to analyze current trends, compare data, and interpret data to make predictions.
- Learning concepts like probability and relative frequency is important to understand statistics and mathematics. Relative frequency and probability are closely related as they both show how frequently an event occurs.
- Mastering relative frequency can help us improve our skills in interpretation and data analysis. It can also be used in the fields of science and economics to analyze trends and patterns. It can lead them to make informed decisions, predict future outcomes, and identify the correlation.
- Students can use the concept of relative frequency in their real-life situations. They can predict the weather and evaluate the results of different surveys. For e.g., if it rains for 6 months a year, then the relative frequency of rain in an entire year can be calculated as 6 / 12 = 0.5 or 50%. This means that the place receives rainfall for half the year.
- They can use the relative frequency to compare their educational patterns and performance over time. They can analyze their scores and grades and they can set goals and decisions for their future purposes.
Tips and Tricks for Finding Relative Frequency
Understanding the tips and tricks for finding the relative frequency will help students interpret data accurately, find the patterns, and solve mathematical problems. A few tips and tricks for calculating relative frequency are:
- Use the correct formula for finding relative frequency. The formula is:
Relative frequency = f / n. Here, f is the frequency and n is the total number of data values given.
- Convert the relative frequency to percentage by multiplying the value with 100.
- The sum of all relative frequencies must be equal to 1 or 100%. If it is greater than 1 or 100%, there is a high possibility of an error in calculations.
- Always remember to add all the given terms to get the total frequencies. If the values are given separately, sum up those terms before calculating relative frequency.
Common Mistakes and How to Avoid Them on How to Find Relative Frequency
To identify patterns and interpret data in statistics and mathematics, we use relative frequency. However, small mistakes in the calculation of relative frequency can lead to incorrect answers and wrong results. Some of the common mistakes and their solutions are given below:
Mistake 1
Using the wrong formula
Students should memorize the correct formula for finding the relative frequency. Sometimes students write the wrong formula, which can lead to an incorrect answer. The correct formula is:
Relative frequency = f / n
Be careful not to change the formula’s structure.
Mistake 2
Forgetting to express relative frequency correctly
Kids should convert the fractions into decimals and percentages. If answers are not simplified or converted, they may become incorrect. For instance, if 50 out of 100 people own a car, then the relative frequency is:
f / n = 50 / 100 = 0.5 or 50%
Writing 50 / 100 without converting it to a percentage or decimal is incomplete.
Mistake 3
Incorrectly adding the relative frequencies
Students should remember to check the sum of all relative frequencies equals 1 or 100%. If the sum of relative frequencies adds up to 150% or more than 100%, then the calculation is incorrect.
Mistake 4
Assuming relative frequency is a raw count
The relative frequency is the proportion and absolute frequency is the raw count. Students tend to wrongly assume that the relative and absolute frequency are interchangeable in a given dataset. To find the relative frequency, we use the formula, f / n.
Mistake 5
Thinking that probability is the same as relative frequency
Students should remember that relative frequency is based on actual data, whereas probability represents the likeliness of an event happening. It is based on the mathematical prediction.
For e.g., when a coin is flipped, the probability of getting a head or a tail is 50%. If the coin is flipped 10 times and we get tails on 4 occasions, then the relative frequency of the occurrence of tails is calculated as 4 / 10 = 0.4 or 40%.
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Solved Examples on Finding Relative Frequency
Problem 1
Virat attended 95 out of 100 school days. Find the relative frequency of his attendance.
95%
Explanation
To find the relative frequency of Virat’s attendance, we can apply the formula:
Relative frequency = f / n
Here, f = 95
n = 100
Now, we can substitute the values:
Relative frequency = 95 / 100 = 0.95
So, Virat’s attendance percentage is 95%. He has a high attendance rate.
Problem 2
A survey of 100 people found that 30 owned a car, 50 owned a bike, and 20 owned no vehicles. Find the relative frequency of each category.
Bike owners: 30%
Car owners: 50%
No vehicles: 20%
Explanation
The formula for finding the relative frequency is: Relative frequency = f / n
The relative frequency of bike owners is:
f = 30
n = 100
So, the relative frequency is, f / n:
30 / 100 = 0.3 or 30%
The relative frequency of car owners is:
f = 50
n = 100
So, the relative frequency is, f / n:
50 / 100 = 0.5 or 50%
The relative frequency of no vehicles is:
f = 20
n = 100
So, the relative frequency is, f / n:
20 / 100 = 0.2 or 20%
So, 50% of the people own a car, 30% own a bike, and 20% don’t own any vehicles.
Problem 3
Anna has 12 pens, 15 pencils, and 10 books. Find the relative frequency of each item.
Relative frequency of pens = 32.4%
Relative frequency of pencils = 40.5%
Relative frequency of books = 27%
Explanation
Here, the given frequency of pens = 12
Frequency of pencils = 15 and
Frequency of books = 10
To find the sum of the frequency of all items, we need to add all the frequencies:
12 + 15 + 10 = 37
Next, the formula for finding the relative frequency is:
Relative frequency = f / n
Therefore, the relative frequency of pens = 12 / 37 = 0.324 or 32.4%
The relative frequency of pencils = 15 / 37 = 0.405 or 40.5%
The relative frequency of books = 10 / 37 = 0.27 or 27%
Problem 4
A coin is tossed 50 times, and heads appear 26 times. What is the relative frequency of heads appearing?
52%
Explanation
Here, the formula to find the relative frequency is: f / n
f = 26
n = 50
Next, we can substitute the values.
Relative frequency = 26 / 50 = 0.52
The relative frequency of heads is 0.52 or 52%.
This means that heads occurred 52% of the time.
Problem 5
In a college of 600 students, 220 students wear uniforms. Find the relative frequency of students who wear uniforms.
36.7%
Explanation
By using the formula, we can find the relative frequency.
Relative frequency = f / n
f = 220
n = 600
So the relative frequency is calculated as: 220 / 600 = 0.367
Therefore, the relative frequency of students wearing a uniform is 0.367 or 36.7%.
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FAQs on How to Find Relative Frequency
1.What is the difference between frequency and relative frequency?
2.What is the formula for calculating relative frequency?
3.Can relative frequency exceed 1?
4.Define the relative frequency table.
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Jaipreet Kour Wazir
About the Author
Jaipreet Kour Wazir is a data wizard with over 5 years of expertise in simplifying complex data concepts. From crunching numbers to crafting insightful visualizations, she turns raw data into compelling stories. Her journey from analytics to education ref
Fun Fact
: She compares datasets to puzzle games—the more you play with them, the clearer the picture becomes!
