## Deciles for grouped data

Deciles are the values of arranged data which divide whole data into ten equal parts. They are 9 in numbers namely $D_1,D_2, \cdots, D_9$. Here $D_1$ is first decile, $D_2$ is second decile, $D_3$ is third decile and so on.

## Formula

For discrete frequency distribution, the formula for $i^{th}$ decile is

### $D_i =\bigg(\dfrac{i(N)}{10}\bigg)^{th}$ value, $i=1,2,\cdots, 9$

where,

• $N$ is total number of observations.

For continuous frequency distribution, the formula for $i^{th}$ quartile is

### $D_i=l + \bigg(\dfrac{\dfrac{iN}{10} - F_<}{f}\bigg)\times h$; $i=1,2,\cdots, 9$

where,

• $l$ is the lower limit of the $i^{th}$ decile class
• $N=\sum f$ total number of observations
• $f$ frequency of the $i^{th}$ decile class
• $F_<$ cumulative frequency of the class previous to $i^{th}$ decile class
• $h$ is the class width