How to calculate percentiles? Formula and procedure explained

Today it is common for us to have to work with large amounts of data, regardless of whether we are dedicated to research or other sectors.

This requires being able to operate with them, often comparing and ordering data with each other. And in this sense, it can be useful to use position measures through which to separate the total values ​​of that measured in various parts to locate in which position one of the they. One of the best known and most useful is the percentile. But... What is a percentile? How to calculate percentiles? Let's see it throughout this article.

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What is a percentile?

One of the most frequent measurements of data position is known as percentile or centile, which involves dividing the total of what is being measured into 99 parts to obtain a total of 100 equal parts. In this way, the totality of what is being measured is represented somewhere in these 99 parts, and the specific data (s) will occupy a position between said 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 some data occupy when the totality of the existing data is divided into one hundred parts, marking the position that leaves below itself a certain percentage of the population corresponding to the value of the percentile per se (that is, for example, percentile 1 is the one that leaves below the 1%). Likewise, it leaves another relevant percentage above itself.

Linked concepts

The concept of percentile is closely linked to that of percentage, but nevertheless they are different concepts: while the percentage is a mathematical calculation that allows us to visualize a certain amount as a fraction of a hundred equal parts, the percentile indicates the position that a piece of data has to occupy to lower the percentage correspondent.

Likewise, the percentile is a value that also is associated with other measures of position, such as quartiles or deciles. The difference lies in the number of divisions and the scale on which we observe where our data is. In fact, the quartiles and deciles correspond to different percentiles, since they are still the position that some data occupy on 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 may not seem like it, can be very useful in many areas. The percentile is still a value that allows us to make comparisons and orders between subjects, cases or degree of existence of a factor or variable in a set, something that allows us to work at a very easily understandable level with more or less extensive data sets and establish a position for the ones we are obtaining.

This, on a practical level, can help us determine, for example, if an attribute or variable is within normal values ​​or if they are below or above the mean. Examples of this are found in that they are helpful in determining whether or not a neuropsychological function is altered, if intelligence levels are found. within normality if we compare the results of a subject with those of its reference population or if a child has a weight and height that is close to or far from the mean for its age.

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Calculate percentiles: how to do it?

Calculating percentiles is a relatively simple process, it is enough to have all the data represented in the same way and carry out a simple calculation. However, this requires not only having specific data, but also being clear about what type of score is going to be ordered and with respect to what and who is going to make the comparison.

In fact, if we use different evaluation instruments, we will frequently see that there are reference tables for assess between which values ​​a given percentile oscillates in order to be able to associate the data obtained experimentally with said percentile. These are carried out with exhaustive measurements with a representative sample of the reference population.

When we have to calculate a percentile it is necessary to take into account in the first place if we are working with ordered or unordered data. When the data is not grouped or ordered, the position in which the percentile is found may calculated by dividing the product of the percentile by the number of elements in the sample from which we started between a hundred. The formula would be P = (k * n) / 100.

When we are facing an ordered data set, we can follow the formula Px = Lri + ((kn / 100 - Fa) / f)(Ac). Thus, it will be enough to add the lower limit of the class where the percentile is the product between the amplitude of the class and the quotient between the subtraction of the position minus the previous accumulated frequency and the frequency total.

Also, find a certain percentile of a data set (for example, find the 25th percentile of a set or database) It only requires dividing the number of values ​​less than the one we have by the total number of values ​​and multiplying this result by one hundred.

Bibliographic references:

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