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:

\[ L_P = \frac{(n+1) k}{100} \]

where \(n\) is the sample size.

How to Compute Percentiles?

• 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:

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

Percentile Interpretation

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 .

Are there multiple ways of computing percentiles?

Observe that there are multiple ways of computing percentiles, depending on the convention used. Even different software's 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 .

Individual vs Grouped Data for Percentiles

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.

Also, observe that this formula applies for sample data. On the other hand, a percentile calculator can work for find EXACT percentiles if you are dealing with a normal distribution and you know the population mean and sd.

Other special types of percentiles

There are some especial types of percentiles that are used frequently to simplify the notation. We have, for example, the quartiles, that divide the distribution in quarters. For example, the first quartile, \(Q_1\) is the same as the 25th percentile. The second quartile, \(Q_2\) is the same as the 50th percentile, and the third quartile, \(Q_3\) is the same as the 75th percentile. You can use this quartile calculator to get those values directly.

You can use our quartile calculator if that that is specifically what you are looking for

What do you need percentiles for?

Percentiles are mostly used to represent a specific "rank" with respect to the rest of the values in the sample. The 90th percentile is interpreted as the value with the property that 90% of the values in the sample are below that specific value.