# How to calculate the percentiles? Formula and procedure

Today it is common for us to have to work with large amounts of data, whether we are engaged in research or in other industries.

To do this, you need to be able to work with them, and often compare and sort the data with each other. And in that sense, it can be useful to use position measurements through which to separate the total values ​​of what is being measured into several parts to locate which position one is in. One of the best known and most useful is the percentile. But … what is a percentile? How to calculate the percentiles? Let’s take a look at it throughout this article.

## What is a percentile?

It is known as the percentile or percentile of one of the most common measures of the position of the data, which involves dividing the total of what is measured into 99 parts to get a total of 100 equal parts. In this way, the whole of what is being measured is represented somewhere in these 99 parts, and the specific data or data will occupy a position between these parts. It is a type of quantile or fractile, values ​​that allow data to be separated into groups with the same number of values.

In other words, percentiles are each of the positions that occupy certain data when all of the existing data is divided into one hundred parts, marking the position that leaves below if at a certain percentage of the corresponding population with the value of the percentile in self (for example, the 1st percentile is the one that leaves below 1%). He also leaves another relevant percentage above himself.

### related concepts

The concept of percentile is closely related to that of percentage, but they are nonetheless different concepts.: While the percentage is a mathematical calculation that allows us to visualize a given amount as a fraction between one hundred equal parts, the percentile tells us the position that a data must occupy to come out below the corresponding percentage.

Likewise, the percentile is a value that also it is associated with other measures of position, such as quartiles or deciles. The difference is in the number of divisions and the scale on which we observe in which position our data is. In fact, quartiles and deciles correspond to different percentiles, because they are always the position occupied by the data at different scales. The different quartiles correspond to the 25th, 50th and 75th percentiles, while the deciles correspond to the 10th, 20th, 30th, 40th, 50th, 60th, 70th and 90th percentiles.

## What are they for?

Knowing what it is and how to calculate a percentile, even if it doesn’t seem to be, can be very helpful in several areas. The percentile is always a value that it allows us to make comparisons and arrangements between subjects, cases or degree of existence of a factor or a variable in a setThis allows us to work at a very understandable level with more or less extensive datasets and establish a position for those we get.

This, from a practical point of view, can help us determine, for example, whether an attribute or variable is within normal values ​​or whether it is below or above the mean. Examples of this are useful in determining whether or not neuropsychological function is impaired, whether intelligence levels are within the normal range if we compare a subject’s results with those of their reference population, or if a child has weight and size. near or far from their average age.

## Calculate percentiles: how to do it?

Calculating percentiles is a relatively straightforward process, sufficient for all data to be represented the same and to perform a simple calculation. However, this requires not only having specific data, but being clear about what type of score is going to be sorted and into what and who is going to compare.

In fact, if we use different evaluation instruments, we will often see that there are reference tables to evaluate between which values ​​a certain percentile oscillates in order to be able to associate the data obtained experimentally with that percentile. these they are carried out with exhaustive measurements with a representative sample of the reference population.

When we need to calculate a percentile, we first need to determine whether we are working with ordered data or not. When the data is not grouped or ordered, the position the percentile is in can be calculated by dividing the product of the percentile by the number of items in the sample from which we start with one hundred. The formula would be P = (k * n) / 100.

When faced with an ordered data set, we can follow the formula Px = LXI + ((kn / 100 – Fa) / f) (Ac). Thus, it will suffice to add the lower limit of the class where there is the percentile to be produced between the amplitude of the class and the quotient between the remainder of the position minus the previous accumulated frequency and the total frequency.

Also, finding a certain percentile of a dataset (for example, finding the 25th percentile of a set or database) only requires dividing the number of values ​​less than what we have for the total number of values ​​and multiply that percentage. result.

#### Bibliographical references:

• Triola, MF (2006). Statistics. Ninth edition. Pearson Education.