S25 — A line where some points count more than others

Twenty-four trees, measured once each: trunk width across the bottom, height up the side. Then you find out the survey did not count them evenly — some trees went into the tally once, some went in many times over. Not one measurement changes. Only how many times each tree counts.

Predict first. Every tree stays exactly where it is on the plot. The only thing that changes is how many times each one is counted. The line through them will:

Who gets counted more

evenly
Try it at both ends and in the middle. 0/3

The same twenty-four trees

counting every tree once: —   |   counting them as the dial says: —

Each circle is one tree; its area is how many times that tree is counted. The grey line counts every tree once. The red line counts them as the dial says.

Push the dial all the way to the wide trunks, so the widest trees count for most and the narrow ones barely count at all. Against the grey line, the red line is: