ABSTRACT
The required average, denoted A, should thus satisfy
ΙΟΟ,ΟΟΟΑ5 = 100,000 x 1.10 x 1.70 x 1.25 x 1.10 x 1.15.
Hence, A5 = 2.9569. A is thus equal to the fifth root of 2.9569 or approximately 1.2421. The computed average, 1.2421, is the geometnc mean of the five numbers 1.10, 1.70, 1.25, 1.10, 1.15. The arith metic mean of these five numbers is 1.26. The arithmetic
m ean, however, is an inappropriate average for th is sit uation because 1 0 0 , 0 0 0 x 1.265 does not equal the sixth year’s sales figure obtained from applying the five yearly increases. Note th a t th e geom etric m ean of these five num bers is sm aller th an their arithm etic mean. This is no accident (see Problem 4.2.6 in P a rt II). More on the geom etric m ean as the m ultiplicative analogue of th e arithm etic m ean (which is based on addition) can be found in Falk (1984) and Usiskin (1974).
