Percentile no. $$$50$$$ of $$$11$$$, $$$8$$$, $$$9$$$, $$$2$$$, $$$11$$$, $$$8$$$, $$$9$$$, $$$5$$$, $$$3$$$
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Your Input
Find the percentile no. $$$50$$$ 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: $$$i = \frac{p}{100} n = \frac{50}{100} \cdot 9 = \frac{9}{2}$$$.
Since the index $$$i$$$ is not an integer, round up: $$$i = 5$$$.
The percentile is at the position $$$i = 5$$$.
So, the percentile is $$$8$$$.
Answer
The percentile no. $$$50$$$A is $$$8$$$A.