### 21.9 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.