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

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

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.