Relative Frequency

The number of times an event occurs is called a frequency. Relative frequency is an experimental one, but not a theoretical one. Since it is an experimental one, it is possible to obtain different relative frequencies when we repeat the experiments. To calculate the frequency we need

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

We can find the relative frequency probability in the following way if we know the above two frequencies. The formula for a subgroup is;

Relative Frequency = Subgroup Count / Total Count

 Related Links Probability Statistics Experimental Probability Events in Probability

How to Calculate Relative Frequency?

The ratio of the number of times a value of the data occurs in the set of all outcomes to the number of all outcomes gives the value of relative frequency.

Let’s understand the Relative Frequency formula with the help of an example

Let’s look at the table below to see how the weights of the people are distributed.

Step 1: To convert the frequencies into relative frequencies, we need to do the following steps.

Step 2: Divide the given frequency bt the total N i.e 40 in the above case(Total sum of all frequencies).

Step 3 : Divide the frequency by total number Let’s see how : 1/ 40 = 0.25.

Example: Let us solve a few more examples to understand the concepts better.

This is a frequency table to see how many students have got marks between given intervals in Maths.

 Marks Frequency Relative Frequency 45 – 50 3 3 / 40 x 100 = 0.075 50 – 55 1 1 / 40 x 100 = 0.025 55 – 60 1 1 / 40 x 100 = 0.075 60 -65 6 6 / 40 x 100 = 0.15 65 – 70 8 8 / 40 x 100 = 0.2 70 – 80 3 3 / 40 x 100 = 0.275 80 -90 11 11 / 40 x 100 = 0.075 90 – 100 7 1 / 40 x 100 = 0.025

It is necessary to know the disparity between the theoretical probability of an event and the observed relative frequency of the event in test trials. The theoretical probability is a number which is calculated when we have sufficient information about the test. If each probable outcome in the sample space is equally likely, then we can consider the number of outcomes of a happening and the number of outcomes in the sample space to calculate the theoretical probability.

The relative frequency is dependent on the series of outcomes resulted in while doing statistical analysis. This frequency can be varied every time we repeat the experiment. The more tests we do during an experiment, the observed relative frequency of an event will get closer to the theoretical probability of the event.

Cumulative Relative Frequency

Cumulative relative frequency is the accumulation of the previous relative frequencies. To obtain that, add all the previous relative frequencies to the current relative frequency. The last value is equal to the total of all the observations. Because all the previous frequencies are already added to the previous total.

Relative Frequency Examples

Example 1: A die is tossed 40 times and lands 6 times on the number 4. What is the relative frequency of observing the die land on the number 4?

Solution: Given, Number of times a die is tossed = 40

Number of positive trial = 6

By the formula, we know,

Relative frequency = Number of positive trial/Total Number of trials

f = 6/40 = 0.15

Hence, the relative frequency of observing the die land on the number 4 is 0.15

Example 2: A coin is tossed 20 times and lands 15 time on heads. What is the relative frequency of observing the coin land on heads?

Solution: Total number of trials = 20

Number of positive trails = 15

By the formula, we know,

Relative frequency = Number of positive trial/Total Number of trials

f = 15/20 = 0.75

Hence, the relative frequency of observing the coin land on heads is 0.75

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