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

The calculator will find the percentile no. $25$ of $8$, $8$, $5$, $-6$, $-6$, $7$, $-7$, $8$, $5$, $2$, $6$, $5$, $7$, $1$, with steps shown.

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### 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.