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 GNU Scientific Library Reference Manual - Third Edition (v1.12) by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. RossiPaperback (6"x9"), 592 pages, 60 figuresISBN 0954612078RRP £24.95 (\$39.95)

20.9 Median and Percentiles

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).

Function: double gsl_stats_median_from_sorted_data (const double sorted_data[], size_t stride, size_t n)
This function returns the median value of sorted_data, a dataset of length n with stride stride. The elements of the array must be in ascending numerical order. There are no checks to see whether the data are sorted, so the function gsl_sort should always be used first.

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.

Function: double gsl_stats_quantile_from_sorted_data (const double sorted_data[], size_t stride, size_t n, double f)
This function returns a quantile value of sorted_data, a double-precision array of length n with stride stride. The elements of the array must be in ascending numerical order. The quantile is determined by the f, a fraction between 0 and 1. For example, to compute the value of the 75th percentile f should have the value 0.75.

There are no checks to see whether the data are sorted, so the function gsl_sort should always be used first.

The quantile is found by interpolation, using the formula

quantile = (1 - \delta) x_i + \delta x_{i+1}


where i is floor((n - 1)f) and \delta is (n-1)f - i.

Thus the minimum value of the array (data[0*stride]) is given by f equal to zero, the maximum value (data[(n-1)*stride]) 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.

 ISBN 0954612078 GNU Scientific Library Reference Manual - Third Edition (v1.12) See the print edition