Data and Displays · Superchallenge problem

A data set contains the value $k$ exactly $k$ times for each $k = 1, 2, \ldots, 20$ (so $210$ values). It is drawn as a histogram with bins $0.5$–$5.5$, $5.5$–$10.5$, $10.5$–$15.5$ and $15.5$–$20.5$. The median is estimated from the histogram by assuming values are spread evenly within each bin (the point where half the area lies to the left). By how much does the true median exceed this estimate?