**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

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:

\[ P_k = P_{low} + (L_P -L_{low})\times(P_{high} - P_{low}) \]