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Few examples are shown here, when there is no zero value in the climatology, so all ensemble forecast members can be ranked without any issue. For simplicity, 5 clusters are used in the forecast only. So, for example in the first row, 10 ensemble members are in the first group, which will all have the rank of 40. Then , again 10 members will be in the 2nd group with the rank of 45, and so on. Then, the rank-mean of this simplified forecast distribution will be very close to 50, as the mean os practically speaking the mean of the rank of the 5 groups with 40, 45, 50, 55 and 60, as the population of the 5 groups is almost exactly the same (other than the middle group with 11).

The even distribution is represented first, for which it is shown that by shifting the same rank distribution up or down does not change the standard deviation (and uncertainty). This is true for any variety of rank distributions. Also, after 'narrowing' the rank distribution, the mean does not change, but the uncertainty drops markedly. Moreover, in a similar manner, by adding extreme members (i.e. 1 or 100 or near that), even if only with very few members (2 in this example below), the uncertainty can be increased quite substantially.