# Percentile no. $$$25$$$ of $$$8$$$, $$$8$$$, $$$5$$$, $$$-6$$$, $$$-6$$$, $$$7$$$, $$$-7$$$, $$$8$$$, $$$5$$$, $$$2$$$, $$$6$$$, $$$5$$$, $$$7$$$, $$$1$$$

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

### Your Input

**Find the percentile no. $$$25$$$ of $$$8$$$, $$$8$$$, $$$5$$$, $$$-6$$$, $$$-6$$$, $$$7$$$, $$$-7$$$, $$$8$$$, $$$5$$$, $$$2$$$, $$$6$$$, $$$5$$$, $$$7$$$, $$$1$$$.**

### 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 $$$-7$$$, $$$-6$$$, $$$-6$$$, $$$1$$$, $$$2$$$, $$$5$$$, $$$5$$$, $$$5$$$, $$$6$$$, $$$7$$$, $$$7$$$, $$$8$$$, $$$8$$$, $$$8$$$.

Since there are $$$14$$$ values, then $$$n = 14$$$.

Now, calculate the index: $$$i = \frac{p}{100} n = \frac{25}{100} \cdot 14 = \frac{7}{2}$$$.

Since the index $$$i$$$ is not an integer, round up: $$$i = 4$$$.

The percentile is at the position $$$i = 4$$$.

So, the percentile is $$$1$$$.

### Answer

**The percentile no. $$$25$$$A is $$$1$$$A.**