Percentile no. $$$75$$$ of $$$35$$$, $$$28$$$, $$$43$$$, $$$32$$$
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Find the percentile no. $$$75$$$ of $$$35$$$, $$$28$$$, $$$43$$$, $$$32$$$.
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 $$$28$$$, $$$32$$$, $$$35$$$, $$$43$$$.
Since there are $$$4$$$ values, then $$$n = 4$$$.
Now, calculate the index: $$$i = \frac{p}{100} n = \frac{75}{100} \cdot 4 = 3$$$.
Since the index $$$i$$$ is an integer, the percentile no. $$$75$$$ is the average of the values at the positions $$$i$$$ and $$$i + 1$$$.
The value at the position $$$i = 3$$$ is $$$35$$$; the value at the position $$$i + 1 = 4$$$ is $$$43$$$.
Their average is the percentile: $$$\frac{35 + 43}{2} = 39$$$.
Answer
The percentile no. $$$75$$$A is $$$39$$$A.