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Quantile of Numbers

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.

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Quantile of Numbers -

Tag(s) : Statistics, Data processing

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# Quantile of Numbers

## Quantiles Calculator

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.

### How to compute a quantile?

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.

### When to use (Per)centiles?

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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