Percentile no. $25$ of $1$, $-5$, $2$, $4$, $-3$, $6$, $7$, $0$, $2$, $5$, $-4$, $7$

The calculator will find the percentile no. $25$ of $1$, $-5$, $2$, $4$, $-3$, $6$, $7$, $0$, $2$, $5$, $-4$, $7$, with steps shown.

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Find the percentile no. $25$ of $1$, $-5$, $2$, $4$, $-3$, $6$, $7$, $0$, $2$, $5$, $-4$, $7$.

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 $-5$, $-4$, $-3$, $0$, $1$, $2$, $2$, $4$, $5$, $6$, $7$, $7$.

Since there are $12$ values, then $n = 12$.

Now, calculate the index: $i = \frac{p}{100} n = \frac{25}{100} \cdot 12 = 3$.

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 $i = 3$ is $-3$; the value at the position $i + 1 = 4$ is $0$.

Their average is the percentile: $\frac{-3 + 0}{2} = - \frac{3}{2}$.

The percentile no. $25$A is $- \frac{3}{2} = -1.5$A.
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