## Percentiles for grouped data

Percentiles are the values which divide whole distriution into **hundred** equal parts. They are 99 in numbers namely `$P_1, P_2, \cdots, P_{99}$`

. Here `$P_1$`

is first percentile, `$P_2$`

is second percentile and so on.

## Formula

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

`$P_i =\bigg(\dfrac{i(N)}{100}\bigg)^{th}$ value, $i=1,2,\cdots, 99$`

where,

- $N$ is total number of observations.

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

`$P_i=l + \bigg(\dfrac{\frac{iN}{100} - F_<}{f}\bigg)\times h; \quad i=1,2,\cdots,99$`

where,

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