1590s, from Middle French médian (15c.) and directly from Latin medianus "of the middle," from medius "in the middle" (from PIE root *medhyo- "middle"). Originally anatomical, of veins, arteries, nerves. Median strip "strip between lanes of traffic" is from 1954.
"a median part," 1540s, from Latin medianus (see median (adj.)). Meaning "middle number of a series" is from 1883.