How to Find Frequency in Statistics

In statistics, frequency refers to the number of times a particular value or event occurs in a data set. For example, if you are counting how many people chose a specific answer in a survey, the number of people who selected that answer is the frequency. It helps to summarize data by showing how often different values appear.

Frequency in Statistics

In statistics, frequency refers to the number of times a value occurs in a set of data.

• Absolute Frequency
• Relative Frequency
• Cumulative Frequency

Absolute Frequency

Absolute frequency refers to the exact number of times a specific value or event occurs in a data set. For example, if 10 people selected "Yes" in a survey, the absolute frequency of "Yes" is 10. It's simply a count of occurrences without any comparison or percentage.

How to Calculate Absolute Frequency?

Let's take an example of the number of cars owned by households.

Consider this data set.

0, 1, 2, 1, 0, 2, 3, 1, 1, 0

Count the occurrence of each value and make a table like below for Absolute Frequency.

Now we have the frequency of each element.

Relative Frequency

Relative frequency is the proportion or percentage of times a specific value or event occurs compared to the total number of occurrences.

For example, if 10 out of 50 people chose "Yes" in a survey, the relative frequency of "Yes" is 10/50 or 20%. It shows how often something happens in relation to the total.

Formula for Relative Frequency

Formula for Relative Frequency is given as:

Relative Frequency = Absolute Frequency/Total Number of Observations.

Let's consider an example for better understanding.

Considering the example taken in absolute frequency:

Total Number of Observations = 10

Calculate Relative Frequencies

• For 0 cars: Relative Frequency = 3/10 =0.3
• For 1 car: Relative Frequency = 4/10 =0.4
• For 2 cars: Relative Frequency = 2/10 =0.2
• For 3 cars: Relative Frequency = 1/10 =0.1

Interpretation of Relative Frequency

We can interpret these calculated relative frequencies as percentages of the whole. For example:

• 0.3 or 30% of households have 0 cars.
• 0.4 or 40% of households have 1 car.
• 0.2 or 20% of the households have 2 cars.
• 0.1 or 10% of the households have 3 cars.

​Note: The sum of the relative frequencies is always 1.

Cumulative Frequency

Cumulative frequency is the running total of frequencies as you move through a data set. It shows how many values fall below or equal to a certain point. For example, if you’re counting test scores, the cumulative frequency tells you how many students scored at or below a certain score.

How to Calculate Cumulative Frequency?

1. Start with the first frequency (or the frequency of the first class or interval).
2. Add this frequency to the next frequency in the dataset.
3. Continue this process until you reach the last frequency.

Let's consider an example for better understanding.

Example: Let’s extend the car example above to calculate cumulative frequencies.

"How many households own this number of cars or fewer?"

• For 0 cars:

Cumulative frequency = 3 (only considering 0 cars)

• For 1 car:

Cumulative frequency = 3 (from 0 cars) + 4 (for 1 car) = 7

• For 2 cars:

Cumulative frequency = 7 (from 0 and 1 car) + 2 (for 2 cars) = 9

• For 3 cars:

Cumulative frequency = 9 (from 0, 1 and 2 cars) + 1 (for 3 cars) = 10

We can represent this in the table as follows:

Related Articles

• Frequency and Relative Frequency
• Absolute Frequency
• Relative Frequency
• Cumulative Frequency 
• Frequency Distribution in Statistics
• Frequency Distribution Table in Statistics