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.
 

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 \(= { f \over n}\),
where f is the frequency of a specific event and n is the total number of observations.


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 \(= { f \over n}\)

Relative frequency \(= {{ 10 \over 40 }}= 0.25\)

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. 
    

Relative Frequency shows how often a particular value or event occurs compared to the total number of observations in any data set. In this section, we will learn the step-by-step methods to calculate relative Frequency. 

• Find the total number of observations by adding all the frequencies in the data set. 
   
• Divide each Frequency by the total number of observations. 

For example, suppose we have data showing the number of people choosing different types of fruit:

Here, the total number of observations is 20
\({\text {Relative frequency }}= {f \over n}\)

Relative Frequency of apple \(= 4 ÷ 20 = 0.2\)
Relative Frequency of banana \(= 6 ÷ 20 = 0.3\)
Relative Frequency of orange \(= 5 ÷ 20 = 0.25\)
Relative Frequency of mango \(=3 ÷ 20 = 0.15\)
Relative Frequency of grapes \(= 2 ÷ 20 = 0.1\)
 

Cumulative relative frequency is the running total of relative frequency for an ordered dataset. It shows the proportion of observations that fall at or below a particular value or category. 

Now, let’s learn how to find the cumulative relative frequency. To find the cumulative relative frequency, follow these steps:

• First, find the relative frequency of the first class. 
   
• Then add the relative frequency of the next value to the previous total. 
   
• Follow the process for all values in the data set.  

For example, find the cumulative relative frequency of the marks data set for students. 

Relative frequency has many important properties that help in analyzing and interpreting data. By understanding these properties, students can easily compare events, identify trends, and apply statistical concepts to real-life situations.

• Relative frequency is always between 0 and 1 when expressed as decimals. If the relative frequency is zero, the event did not occur; if it is 1, it happened in all observations.
   
• The sum of all relative frequencies in a data set equals 1 because they represent proportions of the total observations.
   
• Relative frequency can be represented as a decimal, a fraction, or a percentage.
   
• Relative frequency is based on actual observations, so it may change if the experiment or data collection is repeated.
   
• Relative frequency cannot be negative, since frequencies cannot be less than zero.

Relative frequency becomes much easier by understanding these simple tips and tricks. By learning these tips and tricks, students can easily master relative frequency. 

• When finding relative frequency, always start by finding the total frequency. 
   

• Memorize the formula to find the relative frequency: \({\text {relative frequency}} ={{ frequency \over {\text {total observations}}}}\). 
   

• Teachers can connect relative frequency and probability to show how relative frequency becomes more accurate as the sample size increases. 
   

• Parents can guide children to guess the relative frequency before calculating. This builds intuition and confidence.
   

• Use visual aids like graphs, charts, and diagrams to help students understand how relative frequencies compare.

Relative frequency shows how often an event occurs relative to the total number of observations. It is widely used across different fields to identify patterns, study trends, and support better decision-making.
 

• In weather forecasting, relative frequency is used to calculate how often weather conditions occur. For example, if it rained on 12 of 30 days in a month, the relative frequency of rainfall is \({{12\over 30 }}= {\text { 0.4, or 40% }}\).
   
• Companies use relative frequency in market research to determine the proportion of customers who prefer a particular product. For example, out of 200 customers surveyed, 70 chose product A. The relative frequency is: \({70\over 200} = 0.35 {\text { or }}35\%\).
   
• In sports, relative frequency is used to track the performance patterns of athletes or teams.
   
• Researchers use relative frequency to analyze how often a disease occurs in a population. For example, in a study of 500 people, 40 were found to have a particular allergy. Then the relative frequency is \({40\over 500} = 0.08 {\text { or }} 8\%\).
   
• Factories used relative frequency to assess production consistency by measuring defects.