Storehouses of parchment

[ReneZ]

Your comment below has me confused.
"The more samples you take, the greater the chance that any one of them is at one of the far ends of the probability distribution."

In my view, if there are two or more non-identical sample results, one will be at the earlier end of the time-line and one at the more recent end. Taking more samples is not going to change this. If all samples come from the same source, more samples should tend to form a cluster, while samples from different sources may tend to extend the time-line, if those sources are sufficiently distinct. There's always going to be a sample at either end of the time-line. The choice of method by which the data is interpreted is also going to have some effect on the results. 

This is related to the statistical distribution. What is measured is "fraction of C-14", and this measurement is assumed to have an error that is normally distributed (i.e. Gaussian). If one looks at the point in this distribution, where the probability is 90% that the value is below, and 10% that the value is above, then:
- with one sample the probability is 10% that it is above
- with two samples, the probability that both are below = 0.9*0.9 = 0.81, so the chance is 19% that one or more of them is/are above
- with three samples this becomes 1 - (0.9)**3 = 28%
etc.

In general, every limit is more likely to be exceeded when there are more samples.