Percentile Calculator

Calculate percentiles step by step

For the given set of data, the calculator will find percentile no. pp, with steps shown.

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Your Input

Find the percentile no. 2525 of 11, 44, 3-3, 22, 9-9, 7-7, 00, 4-4, 1-1, 22, 11, 5-5, 3-3, 1010, 1010, 55.

Solution

The percentile no. pp is a value such that at least pp percent of the observations is less than or equal to this value and at least 100p100 - 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 9-9, 7-7, 5-5, 4-4, 3-3, 3-3, 1-1, 00, 11, 11, 22, 22, 44, 55, 1010, 1010.

Since there are 1616 values, then n=16n = 16.

Now, calculate the index: i=p100n=2510016=4i = \frac{p}{100} n = \frac{25}{100} \cdot 16 = 4.

Since the index ii is an integer, the percentile no. 2525 is the average of the values at the positions ii and i+1i + 1.

The value at the position i=4i = 4 is 4-4; the value at the position i+1=5i + 1 = 5 is 3-3.

Their average is the percentile: 432=72\frac{-4 - 3}{2} = - \frac{7}{2}.

Answer

The percentile no. 2525A is 72=3.5- \frac{7}{2} = -3.5A.