Relative Frequency Formula: Calculation & Solved Examples

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Relative Frequency is the ratio of the number of times an event occurs divided by the total number of events occurring in a given scenario.

In order to determine Relative Frequency, two parameters need to be known:

Number of Total Events/Trials
Frequency Count for a Category/Subgroup

Relative Frequency Formula is given as

Relative Frequency = Subgroup Frequency/ Total Frequency

Table of Content

What is Relative Frequency?
Relative Frequency Formula
How to Calculate Relative Frequency?
Relative Frequency Formula Solved Examples
Things to Remember
Previous Years’ Questions
Sample Questions

Key Terms: Relative Frequency, Relative Frequency Formula, Cumulative Relative Frequency, Frequency, Event

What is Relative Frequency?

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Frequency is defined as a way to measure how often a particular event occurs or has been observed.

Relative Frequency is a method to measure how often a particular event occurs against total occurrences.
It is the comparison between the number of times a number has been repeated to the total frequencies of all the numbers.
It is the division between the individual frequency of an object/item by the total number of repetition that has occurred.

Read More:

Relevant Concepts
Frequency Distribution Table	Frequency Distribution Formula	Cumulative Frequency Distribution
Frequency Polygons	Cumulative Frequency Curve	Ratio & Proportion

Relative Frequency Formula

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Relative Frequency is the ratio of the number of times a number has been repeated to the total frequencies of all the numbers.

To calculate Relative Frequency, one must have the given data:

Frequency Count for Total Population
Frequency Count for Subgroup of the Population

Relative Frequency Formula is given as follows:

Relative Frequency = Subgroup Count / Total Count

It can also be written as:

Relative Frequency = f / n

Where

f: Number of Times Data Occurred in an Observation
n: Total Frequencies

Relative frequency formula

Relative Frequency Formula

How to Calculate Relative Frequency?

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In the set of all outcomes, Relative Frequency is the ratio of the number of times a value of the data appears to the total number of outcomes. Here are the steps to calculate Relative Frequency using the Relative Frequency Formula:

Step 1: Divide the given frequency by the total number of students i.e. 20 (Total number of frequencies).
Step 2: It should be divided like this- 3/20 = 0.15
Step 3: To find out Relative Frequency (in %) just multiply it by 100.
Step 4: It should be calculated as 0.15 x 100 = 15%.

Data Value	Frequency	Relative Frequency in Decimal	Relative Frequency in %
2	3	3/20 or 0.15	15%
3	5	5/20 or 0.25	25%
4	3	3/20 or 0.15	15%
5	6	6/20 or 0.30	30%
6	2	2/20 or 0.10	10%
7	1	1/20 or 0.05	05%

Cumulative Relative Frequency

Cumulative Relative Frequency is defined as the accumulation of the previous relative frequencies. In order to obtain that, add all the previous relative frequencies to the current relative frequency. The last value obtained is equal to the sum total of all the observations.

Relative Frequency Formula Solved Examples

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Here are some solved examples on Relative Frequency Formula for a better understanding:

Example 1: A die is tossed 30 times and it lands 5 times on the number 6. Find the relative frequency of the die landing on the number 6.

Solution: Given that,

Number of Times Die is Tossed = 30
Number of Successful Trials of Getting the Number 6 = 5

Using Relative Frequency Formula,

Relative Frequency = Number of Positive Trials / Total Number of Trials

f = 5/ 30 = 16.66%

Thus, the relative frequency of the die landing on the number 6 is 16.66%.

Example 2: Suyash has a packet containing 20 toffees of different colors. She likes the yellow and red ones the most. Tabulated below is the frequency of each different toffee selected as she picked all 20 toffees one by one and finished them all.

Color of Toffee	Yellow	Red	Green	Brown
Frequency	6	6	3	5

Find the relative frequency of the picked candy being one of her favorites.
Find the relative frequency for the brown toffee.

Solution: According to the Relative Frequency Formula,

Relative Frequency = Number of Times the Event has Occurred/Number of Trials

(A) Relative Frequency of Picking Favourite Toffee =

(Frequency of Yellow Toffee + Frequency of Red Toffeee)/ 20 = 12/ 20 = 60%

(B) Relative Frequency of Brown Toffee = Frequency of Brown Toffee/ 20 = 5/ 20 = 25%

Check More:

Relevant Concepts
Ratio Formula	Statistics	Mean Deviation Continuous Frequency Distribution
Mean, Median and Mode	Population Mean Formula	Statistics Formula

Things to Remember

Frequency is the number of times a particular data value occurs in an observation.
Relative Frequency is the ratio of the number of times a data value appears to the total number of outcomes.
Relative Frequency Formula is given as Relative Frequency = Subngroup Frequency / Total Number of Frequencies.
Relative Frequency Formula can also be written as R = f / n
To obtain Relative Frequency in percentage (%), multiply it by 100.

Previous Years’ Questions

If coefficient of variation is 60 and standard deviation is 24… (KCET - 2017)
If the combined mean of two groups is 40/3… (KEAM)
A student scores the following marks in five tests… (JEE Main - 2019)
The mean and variance of 20 observations are found to be… (JEE Main - 2020)
If the sum of the deviations of 50 observations from 30 is… (JEE Main - 2019)
Standard Deviation of n observations… (WBJEE - 2016)
All the students of a class performed poorly in Mathematics… (COMEDK UGET - 2013)
The shortest distance from the point (3,0) to the parabola… (COMEDK UGET - 2005)
If the mean of the squares of first n natural numbers be…
In a group of students, mean weight of boys is 80 kg and mean weight…

Sample Questions

Ques. A die was tossed 50 times, and it showed the number 4 eight times. Find the relative frequency for the number 4? (3 Marks)

Ans. Given that,

Number of Times Die was Tossed = 50
Number of Times 4 Appeared = 8

Using Relative Frequency Formula,

Relative Frequency = Number of Positive Trial / Total Number of Trials

Relative Frequency = 8/50 = 0.15

Ques. A coin showed 15 times heads out of 20 times tossing it. What will be the relative frequency? (3 Marks)

Ans. Given that,

Number of Times Heads Appeared = 15
Total Number of Tosses = 20

Using Relative Frequency Formula,

Relative Frequency = Number of Positive Trials / Total Number of Trials

Relative Frequency(f) = 15/20 = 0.75

Hence, the relative frequency for heads will be 0.75

Ques. What is Relative Frequency Formula? (3 Marks)

Ans. Relative Frequency is defined as the number of times an event occurs divided by the total number of events occurring in a given observation or situation

Relative Frequency Formula is given as:

Relative Frequency = Subgroup Frequency/Total Frequency

It is also expressed as:

Relative Frequency = f / n

Where

f is the Number of Times Data Occurred in an Observation
n is the Total Frequencies.

Ques. A cubical die is tossed 25 times and lands 4 times on the number 2. What is the relative frequency of observing the die land on the number 2? (3 Marks)

Ans. It is given that,

Number of Times Die was Tossed = 25
Number of Times 2 was obtained = 4

Using Relative Frequency Formula,

Relative Frequency = Number of Positive Trial / Total Number of Trials

Relative Frequency = 4/ 25 = 16%

Thus, the relative frequency of observing the die land on the number 2 is 16%

Ques. State the difference between Frequency and Relative Frequency. (2 Marks)

Ans. The main difference between Frequency and Relative Frequency is that Frequency is dependent on the actual values of each class in a statistical data set while relative frequency compares these individual values to the overall sum of all classes concerned in a data set.

Ques. Aman has a packet containing 20 balloons. 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 balloons one by one.
(A) Find the relative frequency of the picked balloon being one of his favorites.
(B) What is the relative frequency of the brown balloon? (3 Marks)

Ans.

Balloon color	Yellow	Red	Green	Brown
Frequency	6	6	3	5

According to the Relative Frequency Formula,

Relative Frequency = Number of Positive Trials / Total Number of Trials

(A) Relative frequency of the picked balloon to be one of his favorites will be:

(Frequency of Yellow Balloon+ Frequency of Red Balloon)/ 20 = 12/ 20 = 60%

(B) Relative frequency of Brown Balloon = Frequency of Brown Balloon/ 20 = 5/ 20 = 25%

Ques. A coin is flipped 90 times, the coin lands on heads 48 times. Find out the relative frequency of the coin landing on tails. (3 Marks)

Ans. Relative Frequency Formula is given as

Relative Frequency = Number of Positive Trials / Total Number of Trials

Number of Times Coin landed on Tails = 100 - 48 = 52 times

Relative Frequency of Coin landing on Tails = 52/100 = 0.52 = 52%

Thus, the relative frequency of the coin landing on tails is 52%.

Ques. Is Relative Frequency and Probability the Same thing? (2 Marks)

Ans. Relative Frequency is calculated on the basis of the experimental probability. Probability is defined as a number between 0 and 1.0 indicating the likelihood of an event to occur. Thus, the probability is defined as the number of times an event occurs divided by the number of opportunities for it to occur. The outcome of this calculation is referred to as the “relative frequency” of the event.

Ques. Ragini has done a poll in her village to learn more about local residents' mobile phone brands. She reports the outcomes as they are shown in the table below.
(A) Calculate the proportion of people in Ragini's village who are using Samsung.
(B) The population of Ragini's village is 1000. Determine the proportion of Nokia users in this village. (3 Marks)

Ans.

Brand	Frequency
Samsung	218
Nokia	42
Moto	740

(A) Given that,

Total People in Ragini’s Village = 218 + 42 + 740 = 1000
Number of Samsung Users = 218

We know that,

Relative Frequency = Number of Positive Trials / Total Number of Trials

Relative Frequency = 218/1000 = 21.8%

Thus, the relative frequency Samsung users in this Village is 21.8%

(B) Given that,

Total Villagers = 1000
Number of Nokia User = 42

We know that,

Relative Frequency = Number of Positive Trials / Total Number of Trials

Relative Frequency = 42/1000 = 4.2%

Hence, the relative frequency of Nokia user in the village is 4.2%.

Ques. Can Relative Frequency be expressed as a Percentage? (2 Marks)

Ans. Relative Frequency is defined as a measure of the number of times that an event occurs out of the total events. It can be generally expressed as a ratio, however, it can be expressed as a percentage. To obtain relative frequency in percentage, multiply it by 100.

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Relative Frequency Formula: Calculation & Solved Examples

What is Relative Frequency?

Relative Frequency Formula

How to Calculate Relative Frequency?

Cumulative Relative Frequency

Relative Frequency Formula Solved Examples

Things to Remember

Previous Years’ Questions

Sample Questions

CBSE CLASS XII Related Questions

1.
A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length.

2.
Using integration, find the area of the region bounded by the curve \( y = x|x| \), the x-axis, and the vertical lines \( x = -2 \) and \( x = 2 \).

3.
Find: \[ \int \frac{x^2}{(x^2-1)(x^2+4)}\,dx \]

4.
Differentiate \( \tan^{-1}\left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) \) with respect to \( \cos^{-1}(x^2) \).

5.
Find:

If the function \[ f(x)= \begin{cases} \frac{\sin x}{x}+\cos x, & x\neq0\\ k, & x=0 \end{cases} \] is continuous at \(x=0\), then find the value of \(k\).

6.
Find:

The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]

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Relative Frequency Formula: Calculation & Solved Examples

What is Relative Frequency?

Relative Frequency Formula

How to Calculate Relative Frequency?

Cumulative Relative Frequency

Relative Frequency Formula Solved Examples

Things to Remember

Previous Years’ Questions

Sample Questions

CBSE CLASS XII Related Questions

1.A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length.

2.Using integration, find the area of the region bounded by the curve \( y = x|x| \), the x-axis, and the vertical lines \( x = -2 \) and \( x = 2 \).

3.Find: \[ \int \frac{x^2}{(x^2-1)(x^2+4)}\,dx \]

4.Differentiate \( \tan^{-1}\left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) \) with respect to \( \cos^{-1}(x^2) \).

5. Find: If the function \[ f(x)= \begin{cases} \frac{\sin x}{x}+\cos x, & x\neq0\\ k, & x=0 \end{cases} \] is continuous at \(x=0\), then find the value of \(k\).

6. Find: The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]

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SUBSCRIBE TO OUR NEWS LETTER

1.
A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length.

2.
Using integration, find the area of the region bounded by the curve \( y = x|x| \), the x-axis, and the vertical lines \( x = -2 \) and \( x = 2 \).

3.
Find: \[ \int \frac{x^2}{(x^2-1)(x^2+4)}\,dx \]

4.
Differentiate \( \tan^{-1}\left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) \) with respect to \( \cos^{-1}(x^2) \).

5.
Find:

If the function \[ f(x)= \begin{cases} \frac{\sin x}{x}+\cos x, & x\neq0\\ k, & x=0 \end{cases} \] is continuous at \(x=0\), then find the value of \(k\).

6.
Find:

The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]