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Percentile no. $$$50$$$ of $$$10$$$, $$$5$$$, $$$0$$$, $$$1$$$, $$$5$$$, $$$9$$$, $$$-3$$$, $$$2$$$

The calculator will find the percentile no. $$$50$$$ of $$$10$$$, $$$5$$$, $$$0$$$, $$$1$$$, $$$5$$$, $$$9$$$, $$$-3$$$, $$$2$$$, with steps shown.

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Find the percentile no. $$$50$$$ of $$$10$$$, $$$5$$$, $$$0$$$, $$$1$$$, $$$5$$$, $$$9$$$, $$$-3$$$, $$$2$$$.

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 $$$-3$$$, $$$0$$$, $$$1$$$, $$$2$$$, $$$5$$$, $$$5$$$, $$$9$$$, $$$10$$$.

Since there are $$$8$$$ values, then $$$n = 8$$$.

Now, calculate the index: $$$i = \frac{p}{100} n = \frac{50}{100} \cdot 8 = 4$$$.

Since the index $$$i$$$ is an integer, the percentile no. $$$50$$$ is the average of the values at the positions $$$i$$$ and $$$i + 1$$$.

The value at the position $$$i = 4$$$ is $$$2$$$; the value at the position $$$i + 1 = 5$$$ is $$$5$$$.

Their average is the percentile: $$$\frac{2 + 5}{2} = \frac{7}{2}$$$.

Answer

The percentile no. $$$50$$$A is $$$\frac{7}{2} = 3.5$$$A.