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 <math>p</math>th percentile is a value such that at most <math>(100p)%</math> of the observations are less than this value and that at most <math>100(1-p)%</math> 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 <math> k = \frac{p(n+1)}{100} </math>, rounded to the nearest integer and then taking the value that corresponds to that rank.<ref>Pottel, Hans. Statistical flaws in Excel. Retrieved on 2006-03-22.</ref> 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

1.) P25 = Q1

2.) P50 = D5 = Q2

3.) P75 = Q3

4.) P100 = D10 = Q4

5.) P10 = D1

6.) P20 = D2

7.) P30 = D3

8.) P40 = D4

9.) P60 = D6

10.) P70 = D7

11.) P80 = D8

12.) 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.