# Percentile no. $75$ of $2$, $10$, $-1$, $-2$, $-10$, $5$, $-8$, $-9$, $-1$, $-1$, $8$, $1$, $8$, $6$, $9$

The calculator will find the percentile no. $75$ of $2$, $10$, $-1$, $-2$, $-10$, $5$, $-8$, $-9$, $-1$, $-1$, $8$, $1$, $8$, $6$, $9$, with steps shown.

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Find the percentile no. $75$ of $2$, $10$, $-1$, $-2$, $-10$, $5$, $-8$, $-9$, $-1$, $-1$, $8$, $1$, $8$, $6$, $9$.

### 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 $-10$, $-9$, $-8$, $-2$, $-1$, $-1$, $-1$, $1$, $2$, $5$, $6$, $8$, $8$, $9$, $10$.

Since there are $15$ values, then $n = 15$.

Now, calculate the index: $i = \frac{p}{100} n = \frac{75}{100} \cdot 15 = \frac{45}{4}$.

Since the index $i$ is not an integer, round up: $i = 12$.

The percentile is at the position $i = 12$.

So, the percentile is $8$.

The percentile no. $75$A is $8$A.