Relative frequencies and cumulative relative frequencies

CFA level I / Quantitative Methods: Basic Concepts / Statistical Concepts and Market Returns / Relative frequencies and cumulative relative frequencies

The relative frequency is the absolute frequency of each interval divided by the total number of observations. It informs us about how much percentage of total observations lie in a particular interval.

The cumulative relative frequency adds up the relative frequencies as we move from the first to the last interval. Let's understand it using an example.

Example 2: Calculating relative frequency and cumulative frequency

The frequency distribution of annual returns of a mutual fund is given in the table below. Calculate and interpret the relative frequency and cumulative frequency for the annual returns. All the returns are in percentage.

Interval	Frequency
-20	2
-12	3
-4	5
4	6
12	3
20	1

Solution:

Interval	Frequency	Relative frequency	Cumulative frequency	Cumulative relative frequency
-20	2	0.10	2	0.10
-12	3	0.15	5	0.25
-4	5	0.25	10	0.50
4	6	0.30	16	0.80
12	3	0.15	19	0.95
20	1	0.05	20	1.00
Total	20

Interpretation: If it is asked that how much probability is there that the fund will return between 4 percent and 12 percent, then we will look at the relative frequency and get the answer as 0.3.

However, if we are asked to calculate the probability that the return will be greater than 4 percent or lesser than or equal to -4 percent, then we will need the help of cumulative relative frequency. To get the probability of return greater than 4 percent we will subtract the probability of return less than 4 percent from 1 to get 0.5 as our answer. The returns that are lesser than or equal to - 4 percent can be directly observed from the table, and it is 0.25.

Previous LOS: Parameter, sample statistic, and frequency distribution

Next LOS: Histogram and frequency polygon