# Deciles and Percentiles

Deciles

Deciles are the partition values which divide the set of observations into ten equal parts. There are nine deciles: ${D_1},{D_2},{D_3}, \ldots ,{D_9}$. The first decile is ${D_1}$, 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

Percentiles are the points which divide the set of observations into one hundred equal parts. These points are denoted by ${P_1},{P_2},{P_3}, \ldots ,{P_{99}}$, 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 ${P_1}$ is calculated as ${P_1} = {\text{Value of }}{\left( {\frac{n}{{100}}} \right)^{th}}{\text{item}}$. We find the group in which the ${\left( {\frac{n}{{100}}} \right)^{th}}$ item lies and then ${P_1}$ is interpolated from the formula.