Percentile

From Wikipedia, the free encyclopedia

1 Definition
2 Relation between percentile, decile and quartile
3 Examples
4 See also
5 References
6 External links

[edit] 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 $(100 p)%$ of the observations are less than this value and that at most $100(1 - p)%$ are greater. (p is a value between 0 and 1)

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.^[1] One alternative method, used in many applications, is to use a linear interpolation between the two nearest ranks instead of 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.

[edit] Relation between percentile, decile and quartile

P25 = Q1
P50 = D5 = Q2
P75 = Q3
P100 = D10 = Q4
P10 = D1
P20 = D2
P30 = D3
P40 = D4
P60 = D6
P70 = D7
P80 = D8
P90 = D9

Note: One quartile is equivalent to 25 percentile while 1 decile is equal to 10 percentile.

[edit] 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.