# Relative frequency distribution

Relative frequency distribution definition:

To understand what is relative frequency distribution, we first need to know what is a frequency distribution.

If some hundreds or thousands of values of a variable have been noted merely in the arbitrary order in which they occur, the mind cannot properly grasp the significance of the record. We must condense the data by some method of ranking or classification before their characteristics can be comprehended.

One way of doing this would be to dichotomise the data by classifying the individuals as A’s or not-A’s, according as the value of the variable exceeded or fell short of some given value. So the variable values are classified into various classes such that each of the class defined a specific interval of the variable values. The interval chosen for classifying is called the class-interval, and the frequency in a particular class-interval is called a class frequency.

The manner in which the class-frequencies are distributed over the class-intervals is spoken of as the frequency distribution of the variable.

Now here if the respective frequencies are replaced by the corresponding relative frequencies, then we call it the relative frequency distribution.

That is how we define relative frequency distribution. But before we go any further, lets clarify what is relative frequency. Relative frequency of a class interval may be defined as the ratio of the class frequency to the total frequency. Therefore if the frequency of a particular class interval is 15 and the total frequency is 100, then the relative frequency for that class would be 15/100 = 0.15. The sum of all such relative frequencies of the distribution should be equal to 1.

Graphing relative frequency distribution:

The relative frequency distribution graph would usually have the variable values along the x axis and the relative frequencies along the y axis. All the y values in this case have to be less than 1. The relative frequency is sometimes also expressed as a percent of the total frequency.

Above is the relative frequency distribution graph of the IQ scores of a group of students.

Relative frequency histogram:

A histogram facilitates comparison among the frequencies for different class intervals. In order to draw a histogram, the class limits are first converted to the corresponding class boundaries and a series of adjacent rectangles, one against each class interval, with class interval as base and the relative frequency as height are erected.

Relative frequency bar chart is very similar to the above histogram, except that usually bar graph is used for discrete distribution.

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