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<h3 class="section">20.9 Median and Percentiles</h3>
<p>The median and percentile functions described in this section operate on
sorted data. For convenience we use <dfn>quantiles</dfn>, measured on a scale
of 0 to 1, instead of percentiles (which use a scale of 0 to 100).
<div class="defun">
— Function: double <b>gsl_stats_median_from_sorted_data</b> (<var>const double sorted_data</var>[]<var>, size_t stride, size_t n</var>)<var><a name="index-gsl_005fstats_005fmedian_005ffrom_005fsorted_005fdata-1857"></a></var><br>
<blockquote><p>This function returns the median value of <var>sorted_data</var>, a dataset
of length <var>n</var> with stride <var>stride</var>. 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 <code>gsl_sort</code> should
always be used first.
<p>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.
</p></blockquote></div>
<div class="defun">
— Function: double <b>gsl_stats_quantile_from_sorted_data</b> (<var>const double sorted_data</var>[]<var>, size_t stride, size_t n, double f</var>)<var><a name="index-gsl_005fstats_005fquantile_005ffrom_005fsorted_005fdata-1858"></a></var><br>
<blockquote><p>This function returns a quantile value of <var>sorted_data</var>, a
double-precision array of length <var>n</var> with stride <var>stride</var>. The
elements of the array must be in ascending numerical order. The
quantile is determined by the <var>f</var>, a fraction between 0 and 1. For
example, to compute the value of the 75th percentile <var>f</var> should have
the value 0.75.
<p>There are no checks to see whether the data are sorted, so the function
<code>gsl_sort</code> should always be used first.
<p>The quantile is found by interpolation, using the formula
<pre class="example"> quantile = (1 - \delta) x_i + \delta x_{i+1}
</pre>
<p class="noindent">where i is <code>floor</code>((n - 1)f) and \delta is
(n-1)f - i.
<p>Thus the minimum value of the array (<code>data[0*stride]</code>) is given by
<var>f</var> equal to zero, the maximum value (<code>data[(n-1)*stride]</code>) is
given by <var>f</var> equal to one and the median value is given by <var>f</var>
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.
</p></blockquote></div>
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