1,5,6,9,12,15,18,20,21,25
how did the allies double check that their sample was not skewed as I described?
These statistical estimations were cross-checked with a broad range of other sources, in an attempt to gather data on everything from the number of tanks produced, to the number of factories in use and a variety of supply chain factors.
It does seem to be a harder problem if are given that they do not start at 1, but that they are consecutive integers. I imagine you might do a similar sort of statistical estimate on the beginning of the range as well as the end of the range. This introduces more uncertainty, but I see no reason why this wouldn't work
[1] two degrees of freedom should be lost due to estimating both M and L, thus subtracting 2.
Let's take the example in the order it was given in the article: 117, 232, 122, 173, 167, 12, 168, 204, 4, 229
First step we would project the maximum to be 117 + 117 / 1 - 1 = 233. Or, if we drew 1 sample from the population, we would expect the "maximum" to be the average case -- the population mean. We take a minus 1 because there's a degree of freedom lost in using the maximum twice in the same formula (handwaving a bit, but that's a straightforward enough answer for now).
With the second case, we have 232 + 232 / 2 - 1, or 347. We would intuitively expect two cases to effectively be distributed evenly across the population, or at 1/3 and 2/3. (The statistics is a bit different due to the MAX operator here, but I won't go into that).
With the third case, we have 232 + 232 / 3 -1 = 309. Note that while this statistic is still higher than the actual population statistic, it is still converging due to the additional case that helps us counterbalance the weight of the previous unusually-high sample case we observed.
Does that help?