A decile of a sorted data set is any of the 9 values that divide the data set into 10 approximately equal parts. It's a special type of quantile, which is any group of data points that divide ordered data into approximately equal parts. Quantiles are used extensively in descriptive statistics, which is a branch of study that quantifies the collection of data. It is important to note that there are various methods for establishing the decile values for a given population.

Examine the reasons for having more than one method of determining the decile values. When the number of population members of a sorted data set is divisible by 10, we can easily place 1/10 of the ranked members into one of the 10 groups. However, the 10 parts of the data set will not be of equal size when the population is not divisible by 10. We therefore need a method that will precisely determine each of the 9 deciles for a population of any number.

Examine one common method for evaluating percentiles. This is given as V = (n+1)(y/100), where V is the value that separates the bottom y per cent of the population from the top (100 -- y) per cent of the ordered population.

Separate the ordered population into two sets using the equation in Step 2. Members of the population with a ranking lower than V will belong to the lower set, and members of the population with a ranking higher than V will belong to the upper set. If V is a whole number, the member with a ranking equal to V will belong to the upper set.

Use the method described in Steps 2 and 3 to calculate the 9 deciles for a data set with population n. Calculate V = (n+1)(y/100) for y = {10,20,30,40,50,60,70,80,90}. For example, V = (n+1)(10/100) = (n+1)/10 for y = 10.

Use the deciles obtained in Step 4 to place each member of the given population into one of the 10 sets. For example, the first set will consist of the members with a ranking less than the first decile of (n+1)/10. The second set will consist of the members with a ranking less than the second decile and greater than or equal to the first decile and so on. The tenth set will therefore consist of members with a ranking greater than or equal to the ninth decile.