Relative frequency

The frequency with which an event occurs is defined as the number of times it occurs. The concept of relative frequency is one that is experimental rather than theoretical. Because it is an experimental method, it is possible to achieve different relative frequencies if we perform the trials several times. In order to compute the frequency, we must first determine how often it occurs.

The frequency distribution for the entire population

The frequency of occurrences for a subset of the population

If we know the frequencies of the two frequencies mentioned above, we can calculate the relative frequency likelihood in the following fashion. 

The following is the formula for a subgroup:

Relative Frequency = Subgroup Count divided by the total number of subgroups.

The formula for Relative Frequency

The number of times an event occurs divided by the total number of occurrences that occur in a given situation can be characterised as the relative frequency of an event occurring.

In order to compute the relative frequency, it is necessary to know two things:

The total number of events/trials that have taken place.

Frequency count for a category/subgroup.

 In this case, the relative frequency formula is as follows:

Relative Frequency = Subgroup frequency/ Total frequency

How to Calculate Relative Frequency?

It is calculated as the ratio of the number of times a particular value of the data happens in the set of all outcomes divided by the total number of outcomes, which is the relative frequency.

In order to better grasp the Relative Frequency formula, let’s look at an example:

Please have a look at the following table to see how the people’s weights have been allocated.

Step 1: It is necessary to do the following steps in order to convert frequencies into relative frequencies.

Step 2: Divide the stated frequency by the entire number of N, which is 40 in the example above (Total sum of all frequencies).

Step 3: Divide the frequency by the total number of occurrences. Let’s have a look at how: One-fortieth of forty equals 0.25.

Example: Let’s work through a few more examples to gain a better understanding of the principles.

Mathematical students can use this frequency table to see how many of their classmates received passing grades between specified intervals.

It is vital to understand the discrepancy between the theoretical probability of an occurrence and the observed relative frequency of the event observed in test trials in order to make accurate predictions. An estimate of theoretical probability is a number that is calculated when enough information about the test has been gathered. If each probable result in the sample space is equally likely, we may compute the theoretical probability by taking into account the number of possible outcomes of an occurrence and the number of possible outcomes in the sample space, respectively.

In statistical analysis, the relative frequency is determined by a series of outcomes that are obtained as a result of the statistical study. Every time we repeat the experiment, we can change the frequency at which we repeat it. The greater the number of tests we conduct during an experiment, the closer the observed relative frequency of an occurrence will be near the theoretical probability of the event occurring.

Cumulative Relative Frequency

The accumulation of earlier relative frequencies is represented by the term cumulative relative frequency. It is possible to reach this result by adding all of the preceding relative frequencies to the current relative frequency. The last value is equal to the sum of all of the observations in the data set. Because all of the preceding frequencies have already been added to the prior total, there is nothing new to add.

Relative Frequency Examples

Example 1: A dice is thrown 40 times and lands on the number 4 six times. What is the likelihood of watching the dice land on the number 4 in a random drawing?

Solution: Given, The number of times a die is thrown equals 40.

The number of successful trials is six.

According to the formula, the relative frequency is equal to the number of positive trials divided by the total number of trials, which is 6/40 = 0.15.

As a result, the probability of watching the die land on the number 4 is 0.15 out of 1,000.

Example 2: A coin is tossed 20 times and 15 of the times it lands on the heads side. Is it possible to estimate the proportional frequency with which the coin lands on heads?

Solution: The total number of trials is twenty.

The total number of positive trials is 15.

We are aware of the formula.

The relative frequency is defined as the number of positive trials divided by the total number of trials. f = 15/20 = 0.75

As a result, the relative frequency of watching the coin land on heads is 0.75 out of every 100 observations.

Conclusion

Within the overall number of observations, a relative frequency reflects how frequently a given type of event occurs within that total number of observations. It is a sort of frequency that makes use of percentages, proportions, and fractions to calculate the frequency. The importance of relative frequency histograms is that the heights of the histograms can be read as probabilities. These probability histograms provide a graphical representation of a probability distribution, which may be used to assess the likelihood that specific outcomes will occur within a particular group of participants.