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Percentile no. $$$95$$$ of $$$4$$$, $$$7$$$, $$$7$$$, $$$10$$$, $$$10$$$, $$$12$$$, $$$12$$$, $$$14$$$, $$$15$$$, $$$67$$$

The calculator will find the percentile no. $$$95$$$ of $$$4$$$, $$$7$$$, $$$7$$$, $$$10$$$, $$$10$$$, $$$12$$$, $$$12$$$, $$$14$$$, $$$15$$$, $$$67$$$, with steps shown.

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Your Input

Find the percentile no. $$$95$$$ of $$$4$$$, $$$7$$$, $$$7$$$, $$$10$$$, $$$10$$$, $$$12$$$, $$$12$$$, $$$14$$$, $$$15$$$, $$$67$$$.

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 $$$4$$$, $$$7$$$, $$$7$$$, $$$10$$$, $$$10$$$, $$$12$$$, $$$12$$$, $$$14$$$, $$$15$$$, $$$67$$$.

Since there are $$$10$$$ values, then $$$n = 10$$$.

Now, calculate the index: $$$i = \frac{p}{100} n = \frac{95}{100} \cdot 10 = \frac{19}{2}$$$.

Since the index $$$i$$$ is not an integer, round up: $$$i = 10$$$.

The percentile is at the position $$$i = 10$$$.

So, the percentile is $$$67$$$.

Answer

The percentile no. $$$95$$$A is $$$67$$$A.