Apart from errors arising in the analytical process, an unavoidable sampling error arises in modal analysis as soon as an area is selected as representative of the rock. The variance Vs of the distribution of this error was estimated (by replication) in twenty analysis situations. The straight line that fits the twenty estimates with least squared deviations is
Vs = sampling variance,
p = estimated percentage present of the mineral estimated in each analysis situation, i — mean intercept cut off by random lines on the mineral estimated,
A = sample area.
The standard deviation of samples approached 2% for quartz even for sample areas as large as 75 cm2, for rocks such as the Wausau granite in which i for quartz= 1.92 mm.