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

The calculator will find the percentile no. $25$ of $23$, $24$, $21$, $20$, with steps shown.

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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: $\frac{20 + 21}{2} = \frac{41}{2}$.

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