The relative frequency of an event is defined as the number of times that the event occurs during experimental trials, divided by the total number of trials conducted.
Relative frequencies are used to construct histograms whose heights can be interpreted as probabilities.
Formula to calculate relative frequency.
Twenty students were asked how many hours they studied per day. Their response was recorded in a frequency distribution table.
| No. of Students. | No. of Hours Studied. (Frequency) |
| 2 | 3 |
| 4 | 2 |
| 5 | 1 |
| 1 | 7 |
| 3 | 5 |
| 5 | 6 |
To get the relative frequency in this case, we will take each frequency divided by the total frequency.
| No. of Students. | No. of hours (Frequency). | Relative Frequency. |
| 2 | 3 | 3 ÷ 24 = 0.125 |
| 4 | 2 | 2 ÷ 24 = 0.083 |
| 5 | 1 | 1 ÷ 24 = 0.042 |
| 1 | 7 | 7 ÷ 24 = 0.292 |
| 3 | 5 | 5 ÷ 24 = 0.208 |
| 5 | 6 | 6 ÷ 24 = 0.250 |
The sum of the relative frequency column should be 1.
Example:
Below is a frequency distribution table representing number of students absent in every grade.
| Grade | No. of students (Frequency) |
| Grade 1 | 10 |
| Grade 2 | 5 |
| Grade 3 | 4 |
| Grade 4 | 6 |
| Grade 5 | 3 |
| Grade 6 | 2 |
| Grade 7 | 1 |
| Grade 8 | 2 |
| Grade 9 | 1 |
| Grade 10 | 1 |
The total frequency or the cumulative frequency in this case is 35. Therefore, to get the relative frequency, we divide each frequency by 35.
| Grade | No. of absentees (Frequency) | Relative Frequency |
| Grade 1 | 10 | 10 ÷ 35=0.28 |
| Grade 2 | 5 | 5 ÷ 35=0.14 |
| Grade 3 | 4 | 4 ÷ 35=0.11 |
| Grade 4 | 6 | 6 ÷ 35=0.17 |
| Grade 5 | 3 | 3 ÷ 35=0.09 |
| Grade 6 | 2 | 2 ÷ 35=0.06 |
| Grade 7 | 1 | 1 ÷ 35=0.03 |
| Grade 8 | 2 | 2 ÷ 35=0.06 |
| Grade 9 | 1 | 1 ÷ 35=0.03 |
| Grade 10 | 1 | 1 ÷ 35=0.03 |
The sum of the relative frequency is 1.
