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- Current: Oct 4, 2020
Percentile
A percentile is one of the measures of spread in statistics. The difinition of the Kth percentile differs depending on whether nK/100 is an integer or not. n refers to the sample number.
- The (m + 1)th largest sample point if nK/100 is not an integer (where m is the largest integer less than nK).
- The average of the (nK/100)th and (nK/100 + 1)th largest observations if nK/100 is an integer.
Two examples are shown below. The 50th percentile is equal to the median.
For example, the 50th percentile of the Example 1 is calculated as follows: n = 5, K = 50, and thus nK/100 = 2.5 (not an integer). Therefore the first definition will be applied.
The m is the largest integer less than 2.5, which is 2. The 50th percentile is the 3rd largest sample point, which is 3.
Example 1: (1, 2, 3, 4, 5)
The 50th percentile of the Example 2 is calculated as follows: n = 6, K = 50, and thus nK/100 = 3 (an integer). Therefore the second definition will be applied.
The 50th percentile is the average of 3rd and 4th largest observations. i.e., average of 3 and 4, which is 3.5.
Example 2: (1, 2, 3, 4, 5, 6)
Definitions in the literature
- ... the pth percentile is the value Vp such that p percent of the sample points are less than or equal to Vp [1].
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