Besides the probable error above considered, there is another quantity ofsome importance in practice, which may be called the Risk of a departurefrom the most probable number of survivers. It is obtained by addingtogether the products of all the possible positive deviations in the numberof the survivers from its most probable value, each multiplied into theprobability of its occurrence; or by adding together the products of all thepossible negative deviations in the number of the survivers from its mostprobable value, each multiplied into the probability of its occurrence; inthis case, however, taken without sign. For if we consider the deviationsfrom the most probable number of survivers, taken without regard to sign, asrepresented by proportional sums of money, then the quantity just definedevidently expresses either the mathematical expectation of gain of a personwho is to receive those sums, or the mathematical expectation of loss of aperson who is to pay them. The latter of these two ideas more generallyoccurs in practice.