The relative frequency distribution is a grouped frequency distribution table that also shows the relative frequencies. The relative frequencies are quantities that tell us what proportion of the total number of values lie within a particular class interval.
How to construct the relative frequency table?
The procedure is to construct the relative frequency table is as follows:
- Construct the grouped frequency table for the data.
- Add up all frequencies to find the total frequency.
- To calculate the relative frequency column simply divide the each frequency by the total frequency that you have already found in step 2.
Example:
Consider the following data about heights of a group of people and their frequencies:
| Class Intervals (Heights in cm) | Frequency (Number of People) |
| 160-165 | 4 |
| 165-170 | 6 |
| 170-175 | 5 |
| 175-180 | 3 |
| 180-185 | 2 |
| TOTAL=20 people |
To find the relative frequency for a particular class interval divide its frequency by the total frequency. So for example to find the relative frequency for 160-165 we simply divide 4 by the total frequency which is 20. So we get the relative frequency for 160-165 as 0.2.
The interpretation of this is that 0.2 or 20% of the total people have heights lying between 160cm and 165cm.
So we obtain the final relative frequency table as:
| Class of Intervals (Heights in cm) | Frequency (Number of People) | Relative frequency |
| 160-165 | 4 | 4/20= 0.2 |
| 165-170 | 6 | 6/20= 0.3 |
| 170-175 | 5 | 5/20= 0.25 |
| 175-180 | 3 | 3/20=0.15 |
| 180-185 | 2 | 2/20=0.1 |
| TOTAL=20 people | TOTAL=1 |
We see that the relative frequencies always add up to 1.
Use or Advantage of relative frequency:
The use of relative frequency is that it tells us what proportion of the data takes the particular value. Merely looking at the frequency does not give us information about the data unless it is compared with the total frequency which is precisely what the relative frequency does.
Using the relative frequency table, we can also construct the relative frequency histogram which helps us in visualizing the data.
Relative Frequency Histogram Example:
Consider the following relative frequency distribution about marks obtained by 100 students in a test worth 40 marks:
The relative frequency histogram looks like,
