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. 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

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.