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Percentile no. $$$48$$$ of $$$3$$$, $$$5$$$, $$$7$$$, $$$2$$$, $$$7$$$, $$$8$$$, $$$1$$$

The calculator will find the percentile no. $$$48$$$ of $$$3$$$, $$$5$$$, $$$7$$$, $$$2$$$, $$$7$$$, $$$8$$$, $$$1$$$, with steps shown.

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Your Input

Find the percentile no. $$$48$$$ of $$$3$$$, $$$5$$$, $$$7$$$, $$$2$$$, $$$7$$$, $$$8$$$, $$$1$$$.

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 $$$1$$$, $$$2$$$, $$$3$$$, $$$5$$$, $$$7$$$, $$$7$$$, $$$8$$$.

Since there are $$$7$$$ values, then $$$n = 7$$$.

Now, calculate the index: $$$i = \frac{p}{100} n = \frac{48}{100} \cdot 7 = \frac{84}{25}$$$.

Since the index $$$i$$$ is not an integer, round up: $$$i = 4$$$.

The percentile is at the position $$$i = 4$$$.

So, the percentile is $$$5$$$.

Answer

The percentile no. $$$48$$$A is $$$5$$$A.