# Percentile Calculator

## Calculate percentiles step by step

For the given set of data, the calculator will find percentile no. $p$, with steps shown.

Related calculators: Five Number Summary Calculator, Box and Whisker Plot Calculator

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Find the percentile no. $25$ of $1$, $4$, $-3$, $2$, $-9$, $-7$, $0$, $-4$, $-1$, $2$, $1$, $-5$, $-3$, $10$, $10$, $5$.

### 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 $-9$, $-7$, $-5$, $-4$, $-3$, $-3$, $-1$, $0$, $1$, $1$, $2$, $2$, $4$, $5$, $10$, $10$.

Since there are $16$ values, then $n = 16$.

Now, calculate the index: $i = \frac{p}{100} n = \frac{25}{100} \cdot 16 = 4$.

Since the index $i$ is an integer, the percentile no. $25$ is the average of the values at the positions $i$ and $i + 1$.

The value at the position $i = 4$ is $-4$; the value at the position $i + 1 = 5$ is $-3$.

Their average is the percentile: $\frac{-4 - 3}{2} = - \frac{7}{2}$.

The percentile no. $25$A is $- \frac{7}{2} = -3.5$A.