Commutative frequency is defined as a frequency of random value below a specific level. It just shows that how often the value of a random variable is different from a specific reference value. An example of cumulative frequency is as follows:
Example:
Frequency: Cumulative frequency:
4 4
5 9 (4 + 5)
3 12 (4 + 5 + 3)
2 14 (4 + 5 + 3 + 2)
6 20 (4 + 5 + 3 + 2 + 6)
4 24 (4 + 5 + 3 + 2 + 6 + 4)
Example:
Frequency: Cumulative frequency:
4 4
5 9 (4 + 5)
3 12 (4 + 5 + 3)
2 14 (4 + 5 + 3 + 2)
6 20 (4 + 5 + 3 + 2 + 6)
4 24 (4 + 5 + 3 + 2 + 6 + 4)