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Percentile no. $$$75$$$ of $$$11$$$, $$$8$$$, $$$9$$$, $$$2$$$, $$$11$$$, $$$8$$$, $$$9$$$, $$$5$$$, $$$3$$$

The calculator will find the percentile no. $$$75$$$ of $$$11$$$, $$$8$$$, $$$9$$$, $$$2$$$, $$$11$$$, $$$8$$$, $$$9$$$, $$$5$$$, $$$3$$$, with steps shown.

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Your Input

Find the percentile no. $$$75$$$ of $$$11$$$, $$$8$$$, $$$9$$$, $$$2$$$, $$$11$$$, $$$8$$$, $$$9$$$, $$$5$$$, $$$3$$$.

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 $$$2$$$, $$$3$$$, $$$5$$$, $$$8$$$, $$$8$$$, $$$9$$$, $$$9$$$, $$$11$$$, $$$11$$$.

Since there are $$$9$$$ values, then $$$n = 9$$$.

Now, calculate the index: $$$i = \frac{p}{100} n = \frac{75}{100} \cdot 9 = \frac{27}{4}$$$.

Since the index $$$i$$$ is not an integer, round up: $$$i = 7$$$.

The percentile is at the position $$$i = 7$$$.

So, the percentile is $$$9$$$.

Answer

The percentile no. $$$75$$$A is $$$9$$$A.