# Percentile no. $61$ of $3$, $5$, $7$, $2$, $7$, $8$, $1$

The calculator will find the percentile no. $61$ of $3$, $5$, $7$, $2$, $7$, $8$, $1$, with steps shown.

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Find the percentile no. $61$ of $3$, $5$, $7$, $2$, $7$, $8$, $1$.

### 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 $1$, $2$, $3$, $5$, $7$, $7$, $8$.

Since there are $7$ values, then $n = 7$.

Now, calculate the index: $i = \frac{p}{100} n = \frac{61}{100} \cdot 7 = \frac{427}{100}$.

Since the index $i$ is not an integer, round up: $i = 5$.

The percentile is at the position $i = 5$.

So, the percentile is $7$.

The percentile no. $61$A is $7$A.