Relative Frequency: Formula, Event & Sample Space

Relative Frequency shows the proportion of the specific events that occurred over the total number of events. It can be used to compare samples of different sizes directly. In statistics, a relative frequency table shows the popularity of a certain type of data based on the population sampled. It is presented in percentage, proportion and decimal form. 

Read More concepts in Probability and Statistics

Key Takeaways: Relative Frequency, Observations, Total Number of Events, Probability, Percentage, Frequency, Random 

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What is Relative Frequency?

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Relative frequency or the empirical probability of an event is the number of outcomes in which a specified event occurs within the total number of trials in an actual experiment. It is not used in a theoretical sample space. The proportions are calculated from experience or observation. 

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Relative Frequency Formula 

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Relative frequency is the ratio of observed frequency over total frequency for any randomly conducted experiment. To calculate relative frequency we need: 

• Frequency count for the total population 
• Frequency count for a subgroup of the population

Relative Frequency = Subgroup frequency/ Total frequency 

Or 

Relative Frequency = f/ n 

Here, 

• f = number of times the event occurred in an observation 
• n = total number of frequencies 

Example: Rahul has won 8 games out of 10 games played. Calculate the winning frequency: 

Step 1: Divide the given frequency f i.e., 8 by the total n, i.e.,10. 

Step 2: You get 8/10 or 4/5. Convert it into a percentage. 

The answer is 20% 

Hence, the winning frequency is 20%. 

Many relative frequencies can be calculated from the same experiment. And the sum of all frequencies should be equal to 1 or 100% 

Example: In a game of chess, you win 6 out of 10 times. The relative frequency of your: 

1. Victory is 6/10 or 60% 
2. Defeat (10-6) is 4/10 or 40% 

When you add both the frequencies you’ll get 6/10+4/10 = 10/10 

i.e., 1 

Or 

60% + 40% = 100%

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Cumulative Relative Frequency

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Cumulative relative frequency of a variable is the sum of all the previous relative frequencies occurring for that variable. The last value obtained is equal to the sum of all relative frequencies. It shows the relationship of the events with each other in a tabular form. 

For instance, Count the number of times digits- 2,4,6,8 occurs in the following set: 

{2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 8, 8, 8} 

 

Here, the cumulative relative frequency of each count is calculated by adding the relative frequency of it with the relative frequencies of the preceding counts. 

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Comparison of Frequency, Relative Frequency, Probability

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The difference between frequency and relative frequency is tabulated below.

The difference between relative frequency and probability is tabulated below.

Also read:

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Things to Remember 

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• Relative frequency is the number of times an event has occurred in relation to the total number of events. It is presented in a percentage form. 
• The formula to calculate relative frequency is 

Relative Frequency = Subgroup frequency/ Total frequency 

Or 

f/ n 

• The cumulative relative frequency of a variable is the sum of all the previous relative frequencies occurring for that variable. 
• Relative frequency is different from probability in the way that it is calculated after a random experiment whereas probability is used for theoretical purposes only. 

Also read: NCERT Solutions for Class 9 Mathematics Chapter 14: STATISTICS

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