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What is the difference between Arithmetic mean and Geometric mean?

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If x, y are two no then AM=(x+y)/2 and GM = (xy)^(1/2).

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Arithmetic mean, generally called simple average, is the average of a set of given numbers. In other words, it is the sum of the given numbers in a set divided by the number of items in that set. For example, arithmetic mean of 2, 5, 6 and 7 is 5. 2+5+6+7 = 20. As there are four numbers, 20/4 = 5 and hence the Arithmetic Mean. On the other hand, Geometric Mean (GM) is the nth root of product of a given set of numbers. Suppose the numbers are 1, 3, 9, 27 and 81, GM is the fifth root (as there are 5 numbers) of the product of the given numbers. 1 × 3 × 9 × 27 × 81 = 59049 is the product. Now let us find the fifth root, 5?59049 = 9. So the GM of 1, 3, 9, 27 and 81 is 9

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Maths and Science Mentor

Arithmetic mean characterizes the average value in data-set while Geometric mean allows to estimate the average growth rate for processes with variable in time growth rate.

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An Arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant and Geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

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AM and GM both meant for average. AM is simple average or mean value of given set of numbers by taking simply sum of the given items divided by total items. While, GM means Nth root of the product of given set of numbers or items. GM mostly useful in calculating percentages to know the growth rate.

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Arithmetic mean A is the number between two numbers a and b so that the three numbers a, A, b together form an Arithmetic Progression. Similarly, Geometric mean G is the number between two numbers a and b so that the three numbers a, G, b together form a Geometric Progression.

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Math & Science Home Tutor

Just for difference - Arithmetic mean of two positive numbers can not be less than geometric mean.

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An arithmetic sequence is a sequence of numbers with the difference between two consecutive terms constant. The difference is called the common difference. A geometric sequence is a sequence with the ratio between two consecutive terms constant. This ratio is called the common ratio.

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