## Octiles for grouped data

Octiles are the values of arranged data which divide whole data into eight equal parts. They are 7 in numbers namely $O_1,O_2, \cdots, O_7$. Here $O_1$ is first octile, $O_2$ is second octile, $O_3$ is third octile and so on.

## Formula

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

### $O_i =\bigg(\dfrac{i(N)}{8}\bigg)^{th}$ value, $i=1,2,\cdots, 7$

where,

• $N$ is total number of observations.

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

### $O_i=l + \bigg(\dfrac{\dfrac{iN}{8} - F_<}{f}\bigg)\times h$; $i=1,2,\cdots,7$

where,

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