Relative Frequency

If you are taking your first course in probability and statistics, you are bound to come across the concept of relative frequency. It is an important concept which is often used while calculating probabilities for any occurrence. In this article I explain what is relative frequency and how to find it using the relative frequency formula.

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 the social sciences including economics. The concept of relative frequency is used in every one of these varied fields to calculate probabilities. Let me define some basic concepts in statistics and probability theory, before we talk about relative frequency.

What is Frequency in Probability & Statistics?
What does frequency mean in statistics or probability theory? 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. 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.

What is Absolute Frequency?
Absolute frequency of the event is the actual number of times the event actually occurs during an experiment. In the above experiment the absolute frequency of the coin falling with its heads up is 4.

What is Relative Frequency?
The relative frequency of an event 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 above example, while the absolute frequency of the heads turning up is 4, the relative frequency is 4/10, which is 2/5. Thus the relative frequency of having heads up as an outcome is 2/5 or 0.4.

Listing the values of frequencies for all possible outcomes of an experiment gives us a relative frequency distribution. By knowing the absolute frequencies, a relative frequency 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.

Relative Frequency Formula
Let us formally define the relative frequency formula which will help in calculation. Here it is:

Relative Frequency of an Event 'A' = (Number of Times the Event A Successfully Occurs) / (Total Number of Events) = n_i / N

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

How to Find Relative Frequency
A look at the formula above should make it clear as to how to find relative frequency of an event. When calculating the relative frequency of 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.

Hope this article has left no doubt in your mind about what is relative frequency and how it's used to solve problems in mathematics. Solve as many examples or problems dealing with relative frequency as you can to get an even better grasp of it.