# Percentile no. $75$ of $15$, $19$, $20$, $25$, $31$, $38$, $41$

The calculator will find the percentile no. $75$ of $15$, $19$, $20$, $25$, $31$, $38$, $41$, with steps shown.

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Find the percentile no. $75$ 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: $i = \frac{p}{100} n = \frac{75}{100} \cdot 7 = \frac{21}{4}$.

Since the index $i$ is not an integer, round up: $i = 6$.

The percentile is at the position $i = 6$.

So, the percentile is $38$.

The percentile no. $75$A is $38$A.