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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.The X-axis of the graph is the ratio of in a closed system over time.It is not easily explained, in the general case, in any other way.There is no good way to tell how close the computed result is likely to be to the actual age.An additional nice feature of isochron ages is that an "uncertainty" in the age is automatically computed from the fit of the data to a line.
The simplest form of isotopic age computation involves substituting three measurements into an equation of four variables, and solving for the fourth.
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...
For further information on fitting of lines to data (also known as regression analysis), see: Note that the methods used by isotope geologists (as described by York) are much more complicated than those described by Gonick.
This will be discussed in more detail in the section on Gill's paper below.