Statistics - Organizing and Interpreting Data

Relative Frequency

When analyzing data distribution, it is sometimes more meaningful to consider the proportion of each frequency in relation to the total, rather than just the raw frequencies. However, frequency distribution tables alone may not make these proportions clear.

To determine the proportion of each class’s frequency relative to the total, we divide the frequency of each class by the total frequency. The resulting value is referred to as the relative frequency of the class.
For example, the table below shows the relative frequencies derived from a frequency distribution table based on a survey of the average daily smartphone usage of 50 students:
Usage Time (minutes) Frequency (students) Relative Frequency
30 60 3 0.06
60 90 5 0.10
90 120 10 0.20
120 150 15 0.30
150 180 11 0.22
180 210 6 0.12
Total 50 1
Usage Time (minutes) Frequency (students) Relative Frequency 30^("or more")∼ 60^("less than") 3 0.06 60 ∼ 90 5 0.10 90 ∼ 120 10 0.20 120 ∼ 150 15 0.30 150 ∼ 180 11 0.22 180 ∼ 210 6 0.12 Total 50 1
Typically, the relative frequency of each class ranges between and , and their total sums to .

Representing Relative Frequency Distribution with Graphs

Just as frequency distribution tables can be visualized with histograms or frequency polygons, relative frequency distribution tables can also be represented graphically. In this case:
  • The horizontal axis represents the class intervals.
  • The vertical axis represents the relative frequencies instead of raw frequencies.
  • The graph is constructed in the same way as a histogram or a frequency polygon.

Comparing Distributions of Two Data Sets with Different Totals

When comparing distributions from two data sets with different total frequencies, comparing relative frequencies is more appropriate than comparing raw frequencies.

For instance, the table below shows the frequency and relative frequency distributions of math scores from two classes, A and B:
Score (points) Frequency
(Class A)		 Frequency
(Class B)		 Relative Frequency
(Class A)		 Relative Frequency
(Class B)
50 60 6 0 0.30 0
60 70 4 4 0.20 0.16
70 80 3 10 0.15 0.40
80 90 4 4 0.20 0.16
90 100 3 7 0.15 0.28
Total 20 25 1 1
Score (points) Frequency<br> (Class A) Frequency<br> (Class B) Relative Frequency <br> (Class A) Relative Frequency<br> (Class B) 50^("or more")∼ 60^("less than") 6 0 0.30 0 60 ∼ 70 4 4 0.20 0.16 70 ∼ 80 3 10 0.15 0.40 80 ∼ 90 4 4 0.20 0.16 90 ∼ 100 3 7 0.15 0.28 Total 20 25 1 1
By plotting the relative frequencies of both classes on the same graph, the following observations can be made:
  • Class A has a higher relative frequency for scores between 70 and 80.
  • Class B has a higher relative frequency for scores between 80 and 90.
In general, plotting the relative frequency distributions of two data sets together makes it easier to visually compare their distributions.