Arithmetic Mean (A.M.) The arithmetic mean (A.M.) of a set of numbers is the average of the numbers in the set. It is calculated by adding up the numbers in...
Arithmetic Mean (A.M.)
The arithmetic mean (A.M.) of a set of numbers is the average of the numbers in the set. It is calculated by adding up the numbers in the set and dividing the sum by the number of numbers in the set.
Geometric Mean (G.M.)
The geometric mean (G.M.) of a set of numbers is the average of the reciprocals of the numbers in the set. It is calculated by taking the reciprocal of the average of the reciprocals of the numbers in the set.
Examples
Arithmetic Mean (A.M.):
The average of the numbers 1, 3, 5, 7 is 5.
The average of the numbers 10, 12, 14, 16 is 14.
Geometric Mean (G.M.):
The average of the reciprocals of the numbers 1/2, 1/4, 1/6, 1/8 is 1/4.
The average of the reciprocals of the numbers 1/10, 1/20, 1/30, 1/40 is 1/20.
Relationship between A.M. and G.M.
The arithmetic mean and the geometric mean are related in the following way:
The average of a set of numbers is the same as the average of the reciprocals of the numbers in the set.
The geometric mean of a set of numbers is the same as the reciprocal of the average of the reciprocals of the numbers in the set