The best replacement for midpoint is median.

The best alternatives to midpoint are rated as following:
★★★★★  median
★★  class mark
★  midpoint
  trapezoidal rule

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Speaking about midpoint, one probably shouldn't forget about line segment.

Other search terms related to midpoint and their ratings are:
★★★★★ line segment
★★★★ endpoints
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midpoint
median
class mark