Our daughter had an injury when she was quite young, and an emergency room doctor said they would treat the injury, “…but in the meantime, keep her calm.” She told us later she thought “meantime was when the big bad wolf comes.” Of course that made me curious about the origin of the expression. Apparently, the origin is a mystery, but “mean” can refer to middle or intermediate. The expression refers to doing something in the interim (intermediate) while waiting for something expected to happen.