Relative Frequency in Statistics: Frequency in mathematics is a measure of how often a quantity is present and represents the chances of occurrence of that quantity. In other words, frequency depicts how many times a particular quantity has occurred in an observation.
Relative Frequency is the frequency of an observation concerning the total number of observations. An object’s relative frequency is calculated using the formula Relative frequency = f/n where f is the frequency of an observation and n is the total frequency of the observation of the data set.
In this article, we will learn in detail about Relative Frequency, its meaning, formulas, examples, and relative frequency distribution.
What is Relative Frequency?
Frequency in mathematics represents the actual occurrence of quantities whereas relative frequency represents the occurrence of quantities relative to each other. Suppose we have a term with frequency f and the total frequency of all the observations is n, then the relative frequency of the given observation is f/n.
Relative Frequency Meaning
Relative Frequency is an extension of frequency where each frequency is represented relative to all the present frequencies of different quantities.
The relative frequency formula is the formula that is used to find the relative frequency of any given statistical data. We know that relative frequency is the number of times an event occurs divided by the ratio of the total event in that case. There are various formulas used to calculate relative frequency and the formulas for relative frequencies are,
Relative Frequency = {Frequency of Given Number(xi)} / {Sum of frequency of All Quantities (x1, x2, x3, x4, x5, x6…….xn)}
In other words, we can say that,
Relative Frequency = Subgroup Count / Total Count
We also calculate the relative frequency by the formula,
Relative Frequency = f/n
where,
- f is Frequency of an Observation
- n is Total Frequency
Relative Frequency Distribution
A relative frequency distribution is a statistical representation that shows the frequency of each unique value or group of values in a dataset as a proportion of the total number of data points. This distribution is particularly useful for understanding the distribution of data across different categories or intervals, especially when comparing datasets of different sizes.
Structure of Relative Frequency Distribution
- Data Classification: The first step is to classify the data into categories or intervals (bins). For continuous data, this might involve grouping data into ranges, such as 0-10, 11-20, etc.
- Frequency Count: Calculate the absolute frequency of each category, which is the number of times each value or range of values appears in the dataset.
- Total Data Points: Sum the frequencies to get the total number of observations in the dataset.
- Relative Frequency Calculation: For each category, divide the frequency by the total number of data points to get the relative frequency. This is often expressed as a percentage or a fraction.
What is the Difference Between Probability and Relative Frequency?
Relative Frequency and Probability both deal with how often an event occurs or is likely to occur, but they are derived from different foundations and used in slightly different contexts. The connection between relative frequency and probability is foundational to many statistical methods and principles. As the number of trials in an experiment increases, the relative frequency of an event tends to approach the theoretical probability of that event. This is a cornerstone of the law of large numbers, which states that the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.
How to Find Relative Frequency?
To calculate the relative frequency of an object we follow the steps added below,
Step 1: Study the given table and find the frequency of the term of which relative frequency we have to found.
Step 2: Find the total frequency of all the terms from the table.
Step 3: Divide the Frequecny of Single Term with the total frequency of all the object to get the required relative frequency.
Various examples are added below that helps the students to get a better idea about the relative frequency formula.
Read More: How to find the Relative Frequency?
Relative Frequency Table
The table that contains the relative frequency of all the given elements is called the relative frequency table.
The table added below shows the weight of 30 students of a class along with its relative frequency table and hence it is a Relative Frequency Table.
|
Weight (in Kg)
|
Frequency
|
Relative Frequency
|
|
50-55
|
9
|
9/30 = 0.3
|
|
55-60
|
7
|
7/30 = 0.2333
|
|
60-65
|
6
|
6/30 = 0.2
|
|
65-70
|
2
|
2/30 = 0.066
|
|
70-75
|
6
|
6/30 = 0.2
|
Cumulative Relative Frequency
Cumulative Relative Frequency is the accumulation of all the relative frequency in any given data set. This is represented in the example added below,
The table added below shows the height of 20 students in a class along with relative frequency, and cumulative frequency.
|
Height (in Cm)
|
Frequency
|
Relative Frequency
|
Cumulative Relative Frequency
|
|
150-160
|
4
|
4/20 = 0.2
|
0.2
|
|
160-170
|
5
|
5/20 = 0.25
|
0.45
|
|
170-180
|
6
|
6/20 = 0.30
|
0.75
|
|
180-190
|
5
|
5/20 = 0.25
|
1
|
Sum of all the Cumulative Relative Frequency of all the elements is always equal to 1.
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Relative Frequency Examples
Example 1: Vaibhav has 5 oranges, 10 mangoes, and 6 bananas. Find the relative frequency of each fruit.
Solution:
Given,
- Frequency of Oranges = 5
- Frequency of Mangoes = 10
- Frequency of Bananas = 6
Sum of frequency of All the Fruits(S) = Frequency of Oranges + Frequency of Mangoes + Frequency of Bananas
S = 5 + 10 + 6
S = 21
Relative Frequency of Oranges = (Frequency of Oranges)/ (Sum of Frequency of All Fruits)
= 5/21
Relative Frequency of Mangoes = (Frequency of Mangoes)/ (Sum of Frequency of All Fruits)
= 10/21
Relative Frequency of Bananas = (Frequency of Bananas)/ (Sum of Frequency of All Fruits)
= 6/21
Example 2: A class has 55 boys and 35 girls. Find the relative frequency of each gender.
Solution:
Given,
- Frequency of Boys = 55
- Frequency of Girls = 35
Sum of Frequency(S) = Frequency of Boys + Frequency of Girls
S = 55 + 35
S = 90
Relative Frequency of Boys = (Frequency of Boys)/ (Sum of Frequency)
= 55/90
Relative Frequency of girls = (Frequency of Girls)/ (Sum of Frequency)
= 35/90
Example 3: Anu has 6 candies, 8 chocolates, 4 toffees, and 8 lollipops. Find the relative frequency of each.
Solution:
Given,
- Frequency of Candies = 6
- Frequency of Chocolates = 8
- Frequency of Toffees = 4
- Frequency of Lollipops = 8
Sum of Frequency(S) = Frequency of Candies + Frequency of Chocolates + Frequency of Toffees + Frequency of Lollipops
S = 6 + 8 + 4 + 8
S = 26
Relative Frequency of Candies = (Frequency of Candies)/ (Sum of Frequency)
= 6/26
Relative Frequency of Chocolates = (Frequency of Chocolates)/ (Sum of Frequency)
= 8/26
Relative Frequency of Toffees = (Frequency of Toffees)/ (Sum of Frequency)
= 4/26
Relative Frequency of Lollipops = (Frequency of Lollipops)/ (Sum of Frequency)
= 8/26
Example 4: Find the relative frequency of each term from the table. The table added below shows the marks scored by 30 students in a test out of 10.
|
Marks
|
Frequency
|
|
5
|
9
|
|
6
|
7
|
|
7
|
6
|
|
8
|
2
|
|
9
|
6
|
Solution:
The relative frequency of all the terms is added in the table below,
Total Frequency = Total Students = 30
|
Marks
|
Frequency
|
Relative Frequency
|
|
5
|
9
|
9/30 = 0.3
|
|
6
|
7
|
7/30 = 0.2333
|
|
7
|
6
|
6/30 = 0.2
|
|
8
|
2
|
2/30 = 0.066
|
|
9
|
6
|
6/30 = 0.2
|
Relative Frequency – Practice Problems
Q1: Find the Relative Frequency of winning of a team if it wins 8 out of 16 matches.
Q2: Find the Relative frequency of 10 year old students if there are 20 students out of which 6 are 10 years old, 5 are 11 year old and 9 are 12 years old.
Q3: Among 50 employees that travel to office by different mode of transport, 10 use car, 20 use bike, 10 use auto rickshaw and 10 walks to office.
Summary – Relative Frequency
Relative frequency is a statistical measure that represents the proportion of a particular observation relative to the total number of observations. It is calculated by dividing the frequency of a specific event (f) by the total frequency of all events (n), using the formula Relative Frequency = f/n. This concept extends the idea of frequency, which counts the actual occurrences of quantities, to compare these occurrences against the entire dataset. Relative frequency distribution further elaborates on this by organizing data into categories or ranges, converting raw frequencies into proportions or percentages to illustrate how each category contributes to the whole dataset. Both relative frequency and probability share a foundational connection in statistical methods, especially highlighted by the law of large numbers, which posits that the relative frequency of an event will approximate its theoretical probability as the number of trials increases. Calculating relative frequency involves identifying the frequency of the targeted event, summing up the total frequencies, and then dividing these figures to find the proportion of the event in question. This method provides a valuable tool for understanding and interpreting data distributions, offering insights into the likelihood and patterns of various occurrences within a given dataset.
FAQs on Relative Frequency
What is Relative Frequency?
Relative Frequency is the ratio of the frequency of the objects and the total frequency of the all the data.
What is the Relative Frequency Formula?
Relative Frequency Formula is added below,
Relative Frequency Formula = f/n
where,
- f is Frequency of an Observation
- n is Total Frequency
Is Relative Frequency similar to Frequency in an Observation?
No, relative frequency is not similar to the frequency of an data. As, relative frequency is the ratio of frequency of an object and total frequency of the data set.
How can we find percentage of Relative Frequency?
We can find percentage of relative frequency by multiplying the relative frequency formula by 100.
What is the Relative Frequency Table?
A frequency table presents how often a particular event occurs in a tabulated manner.
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