**Instructions:** This percentile calculator will calculate a percentile you specify, showing step-by-step, for a sample data set provided by you in the form below:

## More About the Percentile Calculator

The k-th percentile of a distribution corresponds to a point with the property that k% of the distribution is to the left of that value. In the case of sample data, the percentiles can be only estimated, and for that purpose, the sample data is organized in ascending order. Then, the *position* of the k-th percentile \(P_k\) is computed using the formula:

where \(n\) is the sample size.

• If \(L_P\) is integer, then the percentile \(P_k\) is the value located in the position \(L_P\) of the data organized in ascending order.

• If \(L_P\) is NOT integer, then w find the two closest integer positions \(L_{low}\) and \(L_{high}\) so that \(L_{low} < L_P < L_{high}\). For example, if \(L_P = 5.25\), then \(L_{low} = 5\) and \(L_{high} = 6\).

So then, we locate the values in the ascending array in positions \(L_{low}\) and \(L_{high}\), and we call them \(P_{low}\) and \(P_{high}\) respectively, and we estimate (interpolate) the percentile \(P_k\) as:

\[ P_k = P_{low} + (L_P -L_{low})\times(P_{high} - P_{low}) \]The concept of percentile takes a very relevant meaning in things like weight and height information, where percentiles indicates how a person has her height and weight relative to the population. This is especially practical for weight, in which individuals that are in excessively low or excessively large percentiles may need to get some extra care.

You can get a complete list statistics with our descriptive statistics calculator.

Observe that there are multiple ways of computing percentiles, depending on the convention used. Even different softwares use different version to compute percentiles (Excel uses one form and Minitab uses a different form.

This interpolation form seems to be the most intuitive one, because it generalizes the way we compute the median. Another very correct approach is described here.

Notice that this calculator works for individual data. If you have grouped data, it would be appropriate to use a Percentile Rank Calculator for grouped data instead, to deal with the grouped data and use midpoints instead

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