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Percentile no. $$$25$$$ of $$$5$$$, $$$15$$$, $$$18$$$, $$$10$$$, $$$8$$$, $$$12$$$, $$$16$$$, $$$10$$$, $$$6$$$
Related calculators: Five Number Summary Calculator, Box and Whisker Plot Calculator
Your Input
Find the percentile no. $$$25$$$ of $$$5$$$, $$$15$$$, $$$18$$$, $$$10$$$, $$$8$$$, $$$12$$$, $$$16$$$, $$$10$$$, $$$6$$$.
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 $$$5$$$, $$$6$$$, $$$8$$$, $$$10$$$, $$$10$$$, $$$12$$$, $$$15$$$, $$$16$$$, $$$18$$$.
Since there are $$$9$$$ values, then $$$n = 9$$$.
Now, calculate the index: $$$i = \frac{p}{100} n = \frac{25}{100} \cdot 9 = \frac{9}{4}$$$.
Since the index $$$i$$$ is not an integer, round up: $$$i = 3$$$.
The percentile is at the position $$$i = 3$$$.
So, the percentile is $$$8$$$.
Answer
The percentile no. $$$25$$$A is $$$8$$$A.