To measure the time averaged position, we can measure where a certain electron is situated relative to the nucleus. Of course, this electron moves around, and in the case of a 1s electron (an electron with a certain amount of energy) even inside the nucleus. We follow this electron for some time, until it has visited every place it can be. We measure the amount of time it spent in every position, then we sum for every position the amount of time spent in each position, times the position itself. Now we have something that we can express in time-units (for example seconds) times position-units (for example meters). As we expect an average position, we need to only have position units, so we should now divide our expression by time. As we want an average, this time should be the total time spent measuring.
One more not: your time and position should not be expressed in seconds or meters, as those units are far smaller than those encountered in atoms/nuclei.