Absolute Frequency (Calculation, Utility, Examples and Graphic Representation)

The absolute frequency is just one statistic measure used in the field of investigation, is the number of times that a data is repeated in a set of them, the value that is observed in a random experiment for each characteristic, the times that the phases or phenomena that are being observing.

Its use is very common in Descriptive statistics, since through this measure it is possible to know how the observations of the same characteristic are distributed in a sample population.

Therefore, its calculation is very simple, since it only requires the count of the times a characteristic is observed or the times it appears within a data group.

Its representation can be expressed through the following nomenclatures: F_i, x_ior n_i, where the letters f, x, n correspond to the frequency and the letter i represents the i - th iteration of the experiment that is being carried out.

Calculation of Absolute Frequency

There is a very simple way to check the accuracy of your calculation, that is, of all the absolute frequencies of the sample population, and that is by obtaining the sum of all of them.

This means that the sum of each one of the absolute frequencies of the sample, corresponds exactly to the total number of data of the same, this data is represented by N.

This being the case, the formula to calculate the absolute frequency is:

_{i = n}

Ʃ f_i = f₁+ f₂+ f₃ +… + F_n = N

^{i = n}

Utility of Absolute Frequency

The absolute frequency allows:

• Represent graphically the occurrence frequency of each of the sample data, either through frequency histograms, bar graphs, pie charts and others specially designed for each study.
• Learn more about the characteristics of a sample, population and universe.
• Create one frequency table both for quantitative variables and for qualitative variables that can be arranged in order.
• Create frequency tables with discrete variables, those that are ordered from highest to lowest and tables of frequencies with continuous variables, which allow ordering them from lowest to highest and grouping them into classes or intervals.
• Calculate the Accumulated Absolute Frequency and the Relative frequency, all important to complete the frequency table, the calculation of other measurements statistics and the elaboration of their respective graphics

Absolute Frequency Examples

To exemplify the absolute frequency, two forms will be considered, considering the values ​​in discrete variables and continuous variables.

Absolute Frequency Example for Discrete Variables

A company wants to entertain the children of its 20 employees (thus N = 20) and give them a gift, after making the consultation, the following data was obtained:

2, 1, 0, 2, 4, 3, 4, 3, 2, 0, 1, 3, 2, 1, 1, 3, 0, 2, 2, 0

Tabulating the data gives the following table:

Number of children	Fi
0	4
1	4
2	6
3	4
4	2
Total	20

Then it can be verified that all the data have been counted, since the sum of all the absolute frequencies completely coincides with the sample size: Total = 20 is equal to N = 20.

In the same way, the frequency of the number of children of each worker could be determined: 4 employees do not have children, 4 only have 1 child, 6 workers have 2 children, 4 have 3 children and finally 2 of them have 4 children.

Absolute Frequency Example for Continuous Variables

The same company from the previous example also needs to know the height of each of its employees (N is still = 20), in this case the data will be decimal numbers, given this characteristic, it is more comfortable to work with data intervals since otherwise the work of tabulation.

After performing the respective measurements, the following 20 measurements were obtained:

1.67, 1.72, 1.90, 1.76, 1.72, 1.96, 1.78, 1.68, 1.87, 1.84, 1.92, 1.72, 1.71, 1.88, 1.77, 1.66, 1.73, 1.82, 1.90, 1.79

Tabulating the data gives the following table:

Employee Height	fi
[1.60 – 1.70)	3
[1.70 – 1.80)	9
[1.80 – 1.90)	4
[1.90 – 2.00)	4
Total	20

The symbol "[" indicates that the number that follows is included in the category, while the symbol ")" indicates that the number preceding it is not included in the category.

Then it can be verified that all the data, since the sum of all the absolute frequencies completely coincides with the sample size: Total = 20 is equal to N = 20.

In the same way, the frequency of height in workers could be determined: 3 employees have a height between 1.60 and 1.70, 9 workers are between 1.70 and 1.80 tall, 4 employees measure from 1.80 to 1.90 and finally, 4 employees measure from 1.90 to 2.00.

Graphical Representation of the Absolute Frequency

There are different ways to plot the Absolute Frequency, some of them are:

• Sector Diagrams: This graph is made up of a circle, divided into sectors, proportional to the relative frequency it represents.
• Absolute Frequency Histogram: represents each variable in the form of bars, its base is proportional to the respective absolute frequency.
• Polygon or Rectangle Diagrams: performed by drawing lines to join the highest points of the columns of the absolute frequency histogram.