Deciles are the partition values which divide the set of observations into ten equal parts. There are nine deciles: . The first decile is , which is a point which has 10% of the observations below it.
Deciles for Individual Observations (Ungrouped Data)
Quartile for a Frequency Distribution (Discrete Data)
Quartile for Grouped Frequency Distribution
Percentiles are the points which divide the set of observations into one hundred equal parts. These points are denoted by , and are called the first, second, third... ninety ninth percentile. The percentiles are calculated for a very large number of observations like workers in factories and the populations in provinces or countries. Percentiles are usually calculated for grouped data. The first percentile denoted by is calculated as . We find the group in which the item lies and then is interpolated from the formula.