1. In an elevator wherein hall buttons are disposed for hall call registration in halls for a plurality of floors served by a plurality of cages, a group supervision apparatus comprising means to tentatively allot the registered hall calls to respective cages and calculate, based on the tentative cage allotments, predicted service times required for the allotted cage to serve passengers, the predicted service times including riding times, service completion times, and waiting times of passengers, mean value and variance calculation means to calculate a mean value and a variance of the predicted service times for each of the tentative cage allotments, means to set a reference time value on the basis of the predicted service times, means to find a square value of a difference between the reference time value and the mean value of the predicted service times and calculate a ratio of the variance relative to the square value corresponding to each of the tentative cage allotments and further to convert the calculated ratio in accordance with a predetermined assignment estimation function which is monotonically increasing so as to calculate an assignment estimation value for each of the cage allotments, and selection means to assign a cage to serve the passengers on the basis of the assignment estimation values which minimize rate of occurrence of long waiting times.