Percentile

Definition

In descriptive statistics, using the percentile is a way of providing estimation of proportions of the data that should fall above and below a given value. The $p$th percentile is a value such that at most $(100p)\%$ of the observations are less than this value and that at most $100(1-p)\%$ are greater.

Thus:

• The 1st percentile cuts off lowest 1% of data
• The 98th percentile cuts off lowest 98% of data

The 25th percentile is the first quartile; the 50th percentile is the median.

One definition is that the pth percentile of n ordered values is obtained by first calculating the rank $k={\frac {p(n+1)}{100}}$, rounded to the nearest integer and then taking the value that corresponds to that rank. This formula only holds for large n (i.e. assuming that we are looking for the 95th percentile over 15 datas, we will have to find the 15,2th...). One alternative method, used in many application, is to use a linear interpolation between the two nearest ranks instead of the rounding.

Linked with the percentile function, there is also a weighted percentile, where the percentage in the total weight is counted instead of the total number. In most spreadsheet applications there is no standard function for a weighted percentile.

Examples

Educational institutions (i.e. universities, schools...) frequently report admission test scores in terms of percentiles. For instance, assume that a candidate obtained 85 on her verbal test. The question is how did this student compared to all others students? If she is told that her score correspond to the 80th percentile, we know that approximately 80% of the other candidates scored lower than him and that approximately 20% of the students had higher score than her.

When ISPs bill "Burstable" Internet bandwidth, the 95th or 98th percentile usually cuts off the top 5% or 2% of bandwidth peaks in each month, and then bills at the nearest rate. In this way infrequent peaks are ignored, and the customer is charged in a fairer way.

Physicians will often use infant and children's weight and height percentile as a gauge of relative health.

See also

• Quantile
• Quartile
• Summary statistics

The Persian equivalent is صدك Compare with decile: دهك

External links

• Free Online Software (Calculator) computes Percentiles for any dataset according to 8 different percentile definitions.