I’m often asked: What’s the difference between Join and Average?
To set the stage, Join and Average commands are on the Object > Path menu. Select two anchor points with the Direct Selection Tool, then execute the command… And there’s where the differences and similarities come into play.
Join: Combines two open paths or two ends of a single open path. Select two anchor points and choose Object > Path > Join (or CMD+J / CTRL+J), which will join the two anchor points with a straight path segment.
Average: Moves anchor points to the median average location between their original locations either horizontally, vertically, or both. For example: Executing the Average command on a path containing an anchor point at 1‑inch X & Y (1‑inch across and up), and a second anchor point at 2‑inches X & Y, will move both selected anchor points to 1.5‑inches X & Y. Anchor points will sit atop one another, but will not be joined. Thus, averaging anchor points in two disconnected paths or in the same open path, will not close the path. To close it, you must follow up Average with Join.
Or, do them both in one step with CMD+OPT+SHIFT+J / CTRL+ALT+SHIFT+J. This command will use the last chosen Average options (Horizontal, Vertical, or Both) to average while joining; anchor points will move to the median location, but instead of overlapping, they’ll be combined into a single anchor point.