## 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