# Percentile Calculator

## Calculate percentiles step by step

For the given set of data, the calculator will find percentile no. $$$p$$$, with steps shown.

Related calculators: Five Number Summary Calculator, Box and Whisker Plot Calculator

### Your Input

**Find the percentile no. $$$25$$$ of $$$1$$$, $$$4$$$, $$$-3$$$, $$$2$$$, $$$-9$$$, $$$-7$$$, $$$0$$$, $$$-4$$$, $$$-1$$$, $$$2$$$, $$$1$$$, $$$-5$$$, $$$-3$$$, $$$10$$$, $$$10$$$, $$$5$$$.**

### Solution

The percentile no. $$$p$$$ is a value such that at least $$$p$$$ percent of the observations is less than or equal to this value and at least $$$100 - p$$$ percent of the observations is greater than or equal to this value.

The first step is to sort the values.

The sorted values are $$$-9$$$, $$$-7$$$, $$$-5$$$, $$$-4$$$, $$$-3$$$, $$$-3$$$, $$$-1$$$, $$$0$$$, $$$1$$$, $$$1$$$, $$$2$$$, $$$2$$$, $$$4$$$, $$$5$$$, $$$10$$$, $$$10$$$.

Since there are $$$16$$$ values, then $$$n = 16$$$.

Now, calculate the index: $$$i = \frac{p}{100} n = \frac{25}{100} \cdot 16 = 4$$$.

Since the index $$$i$$$ is an integer, the percentile no. $$$25$$$ is the average of the values at the positions $$$i$$$ and $$$i + 1$$$.

The value at the position $$$i = 4$$$ is $$$-4$$$; the value at the position $$$i + 1 = 5$$$ is $$$-3$$$.

Their average is the percentile: $$$\frac{-4 - 3}{2} = - \frac{7}{2}$$$.