Percentile

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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 pth 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. (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.

  • 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.

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.

The Persian equivalent is صدك Compare with decile: دهك

http://www.itl.nist.gov/div898/handbook/prc/section2/prc252.htm

  1. ^ Pottel, Hans. Statistical flaws in Excel. Retrieved on 2006-03-22.

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