# Percentile no. $$$25$$$ of $$$23$$$, $$$24$$$, $$$21$$$, $$$20$$$

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### Your Input

**Find the percentile no. $$$25$$$ of $$$23$$$, $$$24$$$, $$$21$$$, $$$20$$$.**

### 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 $$$20$$$, $$$21$$$, $$$23$$$, $$$24$$$.

Since there are $$$4$$$ values, then $$$n = 4$$$.

Now, calculate the index: $$$i = \frac{p}{100} n = \frac{25}{100} \cdot 4 = 1$$$.

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 $$$i = 1$$$ is $$$20$$$; the value at the position $$$i + 1 = 2$$$ is $$$21$$$.

Their average is the percentile: $$$\frac{20 + 21}{2} = \frac{41}{2}$$$.

### Answer

**The percentile no. $$$25$$$A is $$$\frac{41}{2} = 20.5$$$A.**