Hi there. Im trying to build a kd-tree for searching through a set of points, but am getting confused about the use of 'median' in the wikipedia article. For ease of use, the wikipedia article states the pseudo-code of kd-tree construction as:

function kdtree (list of points pointList, int depth)
{
    if pointList is empty
        return nil;
    else
    {
        // Select axis based on depth so that axis cycles through all valid values
        var int axis := depth mod k;

        // Sort point list and choose median as pivot element
        select median by axis from pointList;

        // Create node and construct subtrees
        var tree_node node;
        node.location := median;
        node.leftChild := kdtree(points in pointList before median, depth+1);
        node.rightChild := kdtree(points in pointList after median, depth+1);
        return node;
    }
}

I'm getting confused about the "select median..." line, simply because I'm not quite sure what is the 'right' way to apply a median here.

As far as I know, the median of an odd-sized (sorted) list of numbers is the middle element (aka, for a list of 5 things, element number 3, or index 2 in a standard zero-based array), and the median of an even-sized array is the sum of the two 'middle' elements divided by two (aka, for a list of 6 things, the median is the sum of elements 3 and 4 - or 2 and 3, if zero-indexed - divided by 2.).

However, surely that definition does not work here as we are working with a distinct set of points? How then does one choose the correct median for an even-sized list of numbers, especially for a length 2 list?

I appreciate any and all help, thanks!

-Stephen