Why is it advantageous to use a relative frequency histogram instead of a frequency histogram?

Relative frequency histograms are important because the heights can be interpreted as probabilities. These probability histograms provide a graphical display of a probability distribution, which can be used to determine the likelihood of certain results to occur within a given population.

To see the difference between frequency and relative frequency we will consider the following example. Suppose we are looking at the history grades of students in 12th grade and have the grades: A, B, C, D, F. The number of each of these grades gives us a frequency for each class:

7 students with an F
9 students with a D
18 students with a C
12 students with a B
4 students with an A

To determine the relative frequency for each class we first add the total number of data points: 7 + 9 + 18 + 12 + 4 = 50. Next we, divide each frequency by this sum 50.

0.14 = 14% students with an F
0.18 = 18% students with a D0.36 = 36% students with a C
0.24 = 24% students with a B
0.08 = 8% students with an A

You can see it is very easy and convinient to analyse the data