Percentile no. $$$50$$$ of $$$1$$$, $$$-5$$$, $$$2$$$, $$$4$$$, $$$-3$$$, $$$6$$$, $$$7$$$, $$$0$$$, $$$2$$$, $$$5$$$, $$$-4$$$, $$$7$$$
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Find the percentile no. $$$50$$$ 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: $$$i = \frac{p}{100} n = \frac{50}{100} \cdot 12 = 6$$$.
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 $$$i = 6$$$ is $$$2$$$; the value at the position $$$i + 1 = 7$$$ is $$$2$$$.
Their average is the percentile: $$$\frac{2 + 2}{2} = 2$$$.
Answer
The percentile no. $$$50$$$A is $$$2$$$A.