What is Relative Frequency And How to Calculate It?

Math is fun; it really is―when you can understand the concepts. If you are taking your first course in probability and statistics, you are bound to come across the concept of relative frequency. This is an important concept which is often used while calculating probabilities for any occurrence.

Probability and statistics, is a branch of mathematics which has the widest range of applicability in fields ranging from the pure sciences, applied sciences, and social sciences including economics. This concept is used in every one of these varied fields to calculate probabilities.

Frequency is the number of times an event occurs in any experiment. For example, consider the experiment to be the tossing of a coin. Let an event be the falling of a coin with the 'Heads' side up. The frequency of the event that the coin falls with the head side up would be the number of times that happens.

Now, out of 10 coin tosses, if the coin falls with its heads up 4 times, then the frequency of that event is 4. Frequencies are often represented with the help of histograms in statistics. It is a graphical representation of the frequency count of each event drawn on a two dimensional graph.

Absolute frequency of the event is the exact number of times the event actually occurs during an experiment. In the earlier experiment, the absolute frequency of the coin falling with its heads up is 4.

It is the ratio of the absolute frequency of a particular successful event, with the total number of events. It is the absolute frequency normalized to the total number of events that occur in the experiment. In the earlier example, while the absolute frequency of the heads turning up is 4―the frequency is 4/10, which is 2/5.

Listing the values of frequencies for all possible outcomes of an experiment gives us a relative frequency distribution. By knowing the absolute values, a table can be constructed. When it comes to analyzing the occurrence of specific data points in a data set, it may be divided in classes or divisions with a maximum and minimum limit for each.

Cumulative relative frequency is the number of times a data point with a value less than maximum value for a class, occurs in a data set.

Let us formally define the formula which will help in calculation. Here it is:

Relative Frequency of an Event 'A' = (# of times the event A successfully occurs) / (total # of events) = n_i / N.

where n_i is the absolute frequency of an event and 'N' is the total number of events.

When calculating it for any event, you have to first calculate the absolute frequency of the occurrence of that event or data point. Then divide that number by the total number of events in the experiment or total set of data points, to get the relative frequency of that event.