# Documentation/Calc Functions/PERCENTILE.INC

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PERCENTILE.INC

## Category:

Statistical Analysis

## Summary:

Calculates the alpha-percentile of data values in an array of numbers. Percentiles can be used to understand the significance of particular values within a data set. The nth percentile of a data set is the value below which n% of the data set lies. This function uses an alpha argument lying in the range 0 to 1 (inclusive), which corresponds to a percentage in the range 0% to 100%. For example, an alpha of 0.5 gives the 50th percentile, also known as the median.

## Syntax:

PERCENTILE.INC(Data; Alpha)

## Returns:

Returns a real number which is the scale value for the specified data set and alpha.

## Arguments:

Data is an array or a reference to the range of cells that represents the array of data.

Alpha is a real number or a reference to the cell containing that number which represents the percentage of the scale between 0 and 1 (inclusive).

• If Alpha is greater than 1 or less than 0 then the function returns an error value.
• If Alpha is not a multiple of 1/(n-1) then the function interpolates to obtain the value between two data points, where n is the total number of data points. For example, if we have a data set with five values, then alpha values of 0, 0.25, 0.5, 0.75, and 1 will pick out the values in the data set in ascending order.

## Additional details:

• Alpha = 0.25 gives the first quartile, Alpha = 0.5 gives the median, and Alpha = 0.75 gives the third quartile.
• For more details on percentiles, visit Wikipedia.
 The difference between PERCENTILE.INC/PERCENTILE and PERCENTILE.EXC is that, in the PERCENTILE.INC function the value of alpha is within the range 0 to 1 inclusive and in the PERCENTILE.EXC function, the value of alpha is within the range 0 to 1 exclusive.

## Examples:

Formula Description Returns
=PERCENTILE.INC(A1:A5;0.4) where A1:A5 contains 5,7,3,2,9 The function calculates the value in the data set, which equals 40% of the total data scale in A1:A5. Here interpolation occurs since Alpha is not a multiple of 1/(5-1) = 0.25. 4.2
=PERCENTILE.INC(A1:A5;1) where A1:A5 contains 5,7,3,2,9 The function calculates the value in the data set, which equals 100% of the total data scale in A1:A5. 9
=PERCENTILE.INC({5;7;3;2;9};0.25) The function calculates the value in the data set, which equals 25% of the total data scale. Here no interpolation occurs since Alpha is a multiple of 1/(5-1) = 0.25 and the function returns an exact value from the data set. 3
=PERCENTILE.INC(A1:A5;1.1) where A1:A5 contains 5,7,3,2,9 The function returns an error value since the Alpha is greater than 1. Err:502

None

PERCENTILE.INC