The median and percentile functions described in this section operate on sorted data. For convenience we use "quantiles", measured on a scale of 0 to 1, instead of percentiles (which use a scale of 0 to 100).
data) |
When the dataset has an odd number of elements the median is the value of element (n-1)/2. When the dataset has an even number of elements the median is the mean of the two nearest middle values, elements (n-1)/2 and n/2. Since the algorithm for computing the median involves interpolation this function always returns a floating-point number, even for integer data types.
data, F) |
There are no checks to see whether the data are sorted, so the function sort should always be used first.
The quantile is found by interpolation, using the formula
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(11.15) |
Thus the minimum value of the array (data[0]) is given by F equal to zero, the maximum value (data[-1]) is given by F equal to one and the median value is given by F equal to 0.5. Since the algorithm for computing quantiles involves interpolation this function always returns a floating-point number, even for integer data types.