# Cumulative frequency definition/Benefits/probability distribution

The **accumulated frequency** is the result obtained from the successive sum of the absolute or relative frequencies, when it is carried out from lowest to highest according to their values. In other words, it is understood as the **number of times that a certain event is repeated in a sample or an experiment. Cumulative frequency definition**

This number of repetitions is called absolute frequency, if this is divided by the size of the sample, the relative frequency is obtained as a result. Following the result of these data, the calculation of two types of accumulated frequencies is determined, these are the **accumulated absolute frequency** and the **accumulated relative frequency** .

## Benefits of cumulative frequency

It is important to note that, when extrapolating the distribution of this type of frequency, certain errors can occur by not making an adequate probability distribution once the range of observations has been exceeded.

To avoid this, it is necessary to apply different methods when carrying out the same procedure. Some include the normal, exponential, Pareto, and Gumbel distribution.

Another option that can be taken into account is the introduction of discontinuity between the data, which is of great benefit in case the extreme values and the distribution are separated from the median mass. Among the uses of the method, the analysis of rainfall in response to changes in behavior according to the influence of currents stands out. ** Cumulative frequency definition**

With the aforementioned, it can be said that carrying out a prediction that is based on the accumulated frequency distribution determines a level of margin of error that is often unacceptable. To reduce these types of results and provide the desired benefits, it is advisable to avoid cases that have different data range conditions if they must be compared.

## How is the cumulative frequency classified?

In the accumulated frequency there are two types, these are the following:

### Cumulative absolute frequency

This has the ability to indicate the amount of absolute frequencies, in order to totalize the events that are ordered in a list, these are usually identical or less than the determined value.

This frequency provides information on the number of times that an event is repeated, when a certain number of circumstantial experiments are carried out. In order to find it, only the absolute frequencies must be accumulated. It can be named with the letters Fi.

Example:

Assume the grades of 20 students:

1,2,8,5,8,3,8,5,6,10,5,7,9,4,10,2,7,6,5,10.

The first thing to do to find the accumulated absolute frequency is to order the data from least to greatest, then they must be tabulated and accumulated. As a result, we have:

Xi = Statistical random variable, exam grade.

Fi = Number of times the exam grade is repeated.

N = 20

It is important that the total of the absolute frequency coincide with the total of the sample, which is totally favorable to be able to verify that it is accumulated correctly. ** Cumulative frequency definition**

### Cumulative relative frequency

In this case, the **accumulated absolute frequency** must be divided by the total sample. Some value of the population or sample (Fi) is calculated among the total of the values that make up said population or sample (N). Then to find it, the relative frequencies must be accumulated, which is qualified with the letters Hi.

Example:

Assume the grades of 20 students:

1,2,8,5,8,3,8,5,6,10,5,7,9,4,10,2,7,6,5,10.

The result is as follows:

Xi = Statistical random variable, corresponds to the grade.

Fi = The number of times the note is repeated.

N = 20

Hi = It is the proportion that will represent the i – th value in the sample.

## How is the cumulative frequency calculated?

In order **to calculate the accumulated frequency** , the data must be sorted first of all from least to greatest. To make it easier and have a better visual image, they have to be placed on a table.

By having these data ordered and tabulated, the accumulated frequency can be obtained by adding each class or group of the sample with the previous one. In detail, the following steps must be followed: ** Cumulative frequency definition**

### Sort the data set

The **data set** is the group of numbers that you are going to work with. These values have to be ordered from lowest to highest.

### Count the absolute frequency of each value

The **frequency of a value** is the number of times that it usually appears. The easiest way to keep track of your data is by creating a table.

You only need to type the value or make a description of what the value measures at the beginning of the first column. You should also write the word frequency at the top of the second column, then fill in the box for each value.

### Find the cumulative frequency of the first value

You should always start with the smallest value in the data set. Because there are no smaller values, the response is the same as the absolute frequency of that value.

### Find the next value of the cumulative frequency

Having the first value, you must continue with the next value in the table. In order to find the accumulated frequency of this value, it will be necessary to add the absolute frequency with the total that has been accumulated so far, that is, the last accumulated frequency found is taken and then the absolute frequency of that value is added. ** Cumulative frequency definition**

### Repeat on each remaining value

You should continue scrolling to the larger values. Each time this process is performed, the accumulated frequency is added to the absolute frequency of the next value.

### Check to see if it’s okay

At the end of the entire process described above, the number of times that each of the variables has been presented must have already been added and the final accumulated frequency will have to be equal to the total number of data points in the set.

## What is the probability distribution?

The objective of formulating the **distribution of the accumulated frequency ****in the statistical field** refers to the distribution of probabilities, in order to be able to make the appropriate references of a certain applicable function in a variable, giving the events a definition about it and the different probabilities that it has a place or space.