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Isochron methods avoid the problems which can potentially result from both of the above assumptions.
In many cases, there are independent cues (such as geologic setting or the chemistry of the specimen) which can suggest that such assumptions are entirely reasonable.
However, the methods must be used with care -- and one should be cautious about investing much confidence in the resulting age...
A routine statistical operation on the set of data yields both a slope of the best-fit line (an age) and a variance in the slope (an uncertainty in the age).
The better the fit of the data to the line, the lower the uncertainty.