To calculate frequency, relative frequency, and cumulative frequency, follow these steps:

1. Frequency

This is simply the count of how often a value or range of values occurs in a dataset.

• Example: If you're analyzing the ages of 10 people and 3 of them are 20 years old, the frequency of "20 years" is 3.

2. Relative Frequency

Relative frequency is the proportion of times a value occurs compared to the total number of observations. It is calculated as:

$\text{Relative Frequency} = \frac{\text{Frequency of the value}}{\text{Total number of observations}}$

• Example: If the frequency of 20 years old is 3 out of a total of 10 people, the relative frequency is:

$\frac{3}{10} = 0.3$

This means that 30% of the people in the dataset are 20 years old.

3. Cumulative Frequency

Cumulative frequency is the running total of frequencies up to a certain point. To calculate it:

• Start with the frequency of the first value.

• Add each subsequent frequency to the previous cumulative total.

• Example: If the frequencies of different age groups are:

  • 20 years: 3
  • 21 years: 4
  • 22 years: 2
  • 23 years: 1

The cumulative frequencies are calculated like this:

• For 20 years: 3 (since it's the first value)
• For 21 years: $3 + 4 = 7$
• For 22 years: $7 + 2 = 9$
• For 23 years: $9 + 1 = 10$

The last cumulative frequency should equal the total number of observations.

Example Table

Age	Frequency	Relative Frequency	Cumulative Frequency
20	3	0.30	3
21	4	0.40	7
22	2	0.20	9
23	1	0.10	10

Tip:

Cumulative frequencies help you understand the distribution by showing how the values accumulate over a dataset.

5 Related Questions:

1. How do you calculate the cumulative relative frequency?
2. How is a frequency distribution different from a probability distribution?
3. How can you graph cumulative frequency using an ogive curve?
4. In which cases is relative frequency more useful than simple frequency?
5. How can you calculate frequency for grouped data?

Would you like more details or have any questions?