A student computes the median of a distribution with the inclusive classes 1-20, 21-40, 41-60, 61-80. He forgets to make them continuous and uses the stated lower limit as l, keeping h = 20. Compared with the correct median, his answer is:

The only quantity the boundary correction changes is $l$. The true lower boundary of, say, 41-60 is $41-0.5=40.5$, half the gap $41-40=1$ below the stated limit. Since Median = $l+\left(\frac{n/2-cf}{f}\right)\times h$ and $n,cf,f$ are untouched, an $l$ that is 0.5 too big makes the median 0.5 too big — in the same direction, not the opposite one. The whole gap is 1, but only half of it is applied to each side, so the error is 0.5 and not 1. And $h$ is 20 either way $(60.5-40.5=20)$, so nothing cancels.