Percentile no. $$$75$$$ of $$$5$$$, $$$18$$$, $$$20$$$, $$$40$$$, $$$75$$$

Find the percentile no. $$$75$$$ of $$$5$$$, $$$18$$$, $$$20$$$, $$$40$$$, $$$75$$$.

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 $$$5$$$, $$$18$$$, $$$20$$$, $$$40$$$, $$$75$$$.

Since there are $$$5$$$ values, then $$$n = 5$$$.

Now, calculate the index: $$$i = \frac{p}{100} n = \frac{75}{100} \cdot 5 = \frac{15}{4}$$$.

Since the index $$$i$$$ is not an integer, round up: $$$i = 4$$$.

The percentile is at the position $$$i = 4$$$.

So, the percentile is $$$40$$$.

The percentile no. $$$75$$$A is $$$40$$$A.