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The mean of the numbers a1, a2, a3, ..., an is equal to (a1 + a2 + a3 +... + an)/n. This number is also called the average or the arithmetic mean.

The geometric mean of the positive numbers a1, a2, a3, ... an is the n-th roots of [(a1)(a2)(a3)...(an)]

Given two positive numbers a and b, suppose that a< b. The arithmetic mean, m, is then equal to (1/2)(a + b), and, a, m, b is an arithmetic sequence. The geometric mean, g, is the square root of ab, and, a, g, b is a geometric sequence. For example, the arithmetic mean of 4 and 25 is 14.5 [(1/2)(4 + 25)], and arithmetic sequence is 4, 14.5, 25. The geometric mean of 4 and 25 is 10 (the square root of 100), and the geometric sequence is 4, 10, 25.

It is a theorem of elementary algebra that, for any positive numbers a1, a2, a3, ..., an, the arithmetic mean is greater than or equal to the geometric mean. That is:

(1/n)(a1, a2, a3, ..., an) ≥ n-th roots of [(a1)(a2)(a3)...(an)]

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โˆ™ 2009-01-01 23:11:31
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Q: What is the Relation between geometric mean and arithmetic mean?
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Related questions

What is the difference between geometric mean and arithmetic mean?

The difference between arithmetic and geometric mean you can find in the following link: "Calculation of the geometric mean of two numbers".


What is arithmetic mean and geometric mean?

The difference between arithmetic and geometric mean you can find in the following link: "Calculation of the geometric mean of two numbers".


Difference between geometric mean and arithimetic mean?

You can find the differences between arithmetic and geometric mean in the following link: "Calculation of the geometric mean of two numbers".


Difference between geometric mean and arith metic mean?

The difference between arithmetic and geometric mean you can find in the following link: "Calculation of the geometric mean of two numbers".


WHAT IS relation between arithmetic mean geometric mean and harmonic mean of two numbers?

If x and y are two positive numbers, with arithmetic mean A, geometric mean G and harmonic mean H, then A &acirc;&permil;&yen; G &acirc;&permil;&yen; H with equality only when x = y.


What is the difference between arithmetic mean and geometric mean?

They differ in formula.


What is a geometric property?

1.The Geometric mean is less then the arithmetic mean. GEOMETRIC MEAN &lt; ARITHMETIC MEAN 2.


Differences between harmonic mean and geometric mean?

The differences between arithmetic and geometric mean you can find in the following link: "Calculation of the geometric mean of two numbers". Cheers ebs


What are the differences between harmonic mean and geometric mean?

You can find the differences between arithmetic and geometric mean in the following link: "Calculation of the geometric mean of two numbers". Cheers ebs


What is an arithmetic-geometric mean?

An arithmetic-geometric mean is a mean of two numbers which is the common limit of a pair of sequences, whose terms are defined by taking the arithmetic and geometric means of the previous pair of terms.


Which is greater the geometric mean or the arithmetic mean of 6 and 54?

The geometric mean, if it exists, is always less than or equal to the arithmetic mean. The two are equal only if all the numbers are the same.


What is arithmetic to geometric mean?

You can see the difference in the following link: "Calculation of the geometric mean of two numbers".


If harmonic mean and geometric mean of two numbers are 3.2 and 4 find their arithimetic mean and the two numbers?

Two numbers: 3.2 and 4: Geometric mean is 3.5777087639996634 Arithmetic mean is 3.6 Scroll down to related links and look at "Geometric and Arithmetic Mean".


What is the geometric mean of 0 0 0 1?

0.25..? arithmetic mean...?


Can the arithmetic mean be converted into the geometric mean without having the original data?

Let me clarify. I only have the arithmetic mean. I don't have the data from which it was determined.


What are averages measures of central tendency?

The arithmetic mean, geometric mean and the harmonic mean are three example of averages.


Can a mean have more than one value?

There is one arithmetic mean and one geometric mean to a set of numbers.


What is the (mean) of 120 and 160?

The arithmetic mean is 140. The geometric mean is approx 138.56 and the harmonic mean is approx 137.14


When would you use the geometric mean vs arithmetic mean?

http://www.math.utoronto.ca/mathnet/questionCorner/geomean.html


Q4 The arithmetic mean of 2 numbers is 34 and their geometric mean is 16 One of the numbers will be?

4


What does the word mean mean in mathematical terms?

"Arithmetic mean" means the same as average. "Mean", without qualifiers, usually refers to the arithmetic mean. However, there are other types of "means", for example, the geometric mean.


Can difference between AP series and GP series?

Succession of numbers of which one number is designated as the first, other as the second, another as the third and so on gives rise to what is called a sequence. Sequences have wide applications. In this lesson we shall discuss particular types of sequences called arithmetic sequence, geometric sequence and also find arithmetic mean (A.M), geometric mean (G.M) between two given numbers. We will also establish the relation between A.M and G.M


What does mean equal?

There are three kinds of mean (arithmetic, geometric and harmonic), the first one that you wold come across is the arithmetic mean which is the same as the average.Given a set of values, the [arithmetic] mean is their sum divided by the number of values. All three are measures of central tendency - the value around which observations may be found.There are three kinds of mean (arithmetic, geometric and harmonic), the first one that you wold come across is the arithmetic mean which is the same as the average.Given a set of values, the [arithmetic] mean is their sum divided by the number of values. All three are measures of central tendency - the value around which observations may be found.There are three kinds of mean (arithmetic, geometric and harmonic), the first one that you wold come across is the arithmetic mean which is the same as the average.Given a set of values, the [arithmetic] mean is their sum divided by the number of values. All three are measures of central tendency - the value around which observations may be found.There are three kinds of mean (arithmetic, geometric and harmonic), the first one that you wold come across is the arithmetic mean which is the same as the average.Given a set of values, the [arithmetic] mean is their sum divided by the number of values. All three are measures of central tendency - the value around which observations may be found.


What is the mathematical definition of means?

They are averages of different kinds: arithmetic mean, geometric mean, harmonic mean are three commonly used means.


What is the geometric means between 2 and 24?

Geometric mean between 2 and 24 is 6.928203230275509. Look at link: "Calculation of the geometric mean of two numbers".