Percentile no. $$$25$$$ of $$$15$$$, $$$19$$$, $$$20$$$, $$$25$$$, $$$31$$$, $$$38$$$, $$$41$$$
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Find the percentile no. $$$25$$$ of $$$15$$$, $$$19$$$, $$$20$$$, $$$25$$$, $$$31$$$, $$$38$$$, $$$41$$$.
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 $$$15$$$, $$$19$$$, $$$20$$$, $$$25$$$, $$$31$$$, $$$38$$$, $$$41$$$.
Since there are $$$7$$$ values, then $$$n = 7$$$.
Now, calculate the index: $$$i = \frac{p}{100} n = \frac{25}{100} \cdot 7 = \frac{7}{4}$$$.
Since the index $$$i$$$ is not an integer, round up: $$$i = 2$$$.
The percentile is at the position $$$i = 2$$$.
So, the percentile is $$$19$$$.
Answer
The percentile no. $$$25$$$A is $$$19$$$A.