Among various representative value indicators, mid-range (MR) has the disadvantage of being vulnerable to outliers, and is rarely used today. The MR index is one of the promising models used by humans to intuitively find the representative value of multiple observation values.

However, it is not efficient to use only the maximum and minimum values, so there is a possibility that the MR index can be an inappropriate model for small size data set.

In this study, we propose to treat a data set as nested range values and then calculate a weighted averaging value as new representative value indexes by combining the ranges with the set of weights created according to the definitions.

Among the four proposed models, the special extended mid-range index, which is named XMR, was selected as a model that does not require sorting of observation data. Then, its relative properties compared with traditional representative indexes (mid-range, mean, median, Hodges–Lehmann estimators) were investigated by a simple Monte Carlo simulation using exponential random numbers. Furthermore, preliminary psychological experiment was conducted, which resembled the situation of the simulation. The subjects were asked to reply their estimated representative value by intuition after reading 10 numbers which are assumed to note the intervals between severe accidents or disasters. The result of the experiment suggested that the differences among subjects’ estimation could be fairly large.