# Decile

A decile, in descriptive statistics, is one of the nine values that divide, into ten equal parts, a group of ordered data.

The decile, therefore, is nothing more than a type of quantile, or a series of partitions that are carried out in the data of a sample or population.

In addition, these must be ordered from smallest to largest. In this way, the decile will also go in that same order.

## How is the decile calculated?

The decile, like any other quantile, can be calculated for grouped or non-grouped data. For the former, there are certain formulas that we can find in basic statistics manuals. For the latter, the process is relatively simpler, especially if we have a spreadsheet. In the example we will see this in a little more detail.

We must say that, in the case of non-grouped data, a mathematical expression is used to locate the value of said decile. This is relatively simple, since it is based on the fact that all nine parts of the distribution are the same size.

Therefore, what is done is to use the concrete value if we obtain a whole number, or an average, if the number has decimals.

Let's see a graphical representation of this non-central position measure with the formula that we can use in a spreadsheet:

## Decile characteristics

Deciles have a series of characteristics, such as the ones shown below:

- As position statistics, they are useful for understanding where data is in a distribution. Thus, decile 8 is the upper limit of the data that represent 80% of the total.
- On the other hand, they allow knowing which of them are at the highest levels (> 90%) and at the lowest (<10%).
- They are very frequent in economic comparisons, such as levels of income, wages or income.
- In addition, together with the quartiles, quintiles or percentiles, they are the most used quantiles in descriptive statistics.

## Deciles example

Let's imagine that we want to study the annual per capita income in a country (with fictitious data). To do this, we have chosen a sample that, in turn, we have grouped into certain mean values.

Next, we calculate this statistic and observe what happens, being able to obtain relevant information. In the example, we are going to use the euro as the reference currency.

Looking at the example, first of all, we see that the 10% of the population with the lowest income stands at just under € 5,000. On the other hand, on the opposite side, the 90% who enter the most, get € 12,297. With these data, we can check the difference between the two.

In this way, too, the median would be € 7,606 and corresponds to decile five (D5). This would indicate the median salary of the country.

In short, and as we can see, we are talking about a very useful concept for analysis.

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