Tool to calculate the quantile value from a list of values. The quantiles/percentiles/fractiles of a list of numbers are statistical values that partially illustrates the distribution of numbers in the list.

Quantile of Numbers - dCode

Tag(s) : Statistics, Data processing

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Tool to calculate the quantile value from a list of values. The quantiles/percentiles/fractiles of a list of numbers are statistical values that partially illustrates the distribution of numbers in the list.

From a list of $ n $ values $ A = \{a_1, a_2, \dots, a_n \} $ sorted in ascending order, a **quantile** divides the series and presents the values $ a_i $ at the cutting point in order to retranscribe the distribution of the series of values.

To calculate a **quantile**, sort the list in ascending order and cut it to the corresponding percentile / percent $ n \times p\% $

Example: The list of 7 elements (numbers): 111,10,101,100,11,1,110 is sorted in ascending order 1,10,11,100,101,110,111. Its median (50 percentile) is 100 (middle value), so there are 3 smaller values and 3 values larger than 100 in the list).

NB : the mean is 63.

According to the numbers studied, the cut is variable.

50% (median) allows to locate the middle of the distribution (used for wages, size measurements, weight, etc.)

The 95% and 99% percentiles used for the more numerous statistical phenomena (which therefore make it possible to find the rarest among them) in order to deduce warning values.

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Source : https://www.dcode.fr/numbers-quantile

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