How to Calculate the Geometric Mean
Geometric Mean Help
Two Numbers: Simple Method
Find the numbers you wish to average.
- Ex. 2 and 32.
Two Numbers: Detailed Method
Plug your numbers into the equation below.If your numbers are 10 and 15, for example, plug in 10 and 15 as shown in the picture.
Solve for x.Start by cross-multiplying, which means multiplying the pairs of numbers diagonal to one another and then setting the results on opposite sides of an = sign. Since x*x is x2, your equation should look like: x2= (product of your other numbers). To solve for x, find the square root of your product. If you’re lucky, the results will be a whole number. If not, you can provide a decimal answer or leave your answer in square root form, depending on what your instructor prefers. The example here is in simplified square root form.
Three or More Numbers: Simple Method
Plug your numbers into the equation below.Mean = (a1× a2×. . .× an)1/n
- a1is your first number, a2is your second number, and so forth
- n is the number of entries
Multiply the numbers a1, a2, etc.together.
Calculate thenth root of this number.This is the geometric mean.
Three or More Numbers: Using Logarithms
Find the log of each number and add the logarithmic values together.Find the LOG button on your calculator. When you’re ready, type:(first number) LOG + (second number) LOG + (third number) LOG [+ log of additional numbers as necessary] =. Do not neglect to type=or the number you see will be the log of the most recent number, not the total.
- Ex. log 7 + log 9 + log 12 = 2.878521796…
Divide the sum of the logarithmic values by the number of values you added.If you added the logs of three numbers, divide by three.
- Ex. 2.878521796 / 3 = .959507265…
Find the antilog of your result.On your calculator, press the2ndfunction (usually yellow) and thenLOGto activate the secondary function of the log button, or the antilog. This resulting value is the geometric mean.
- Ex. antilog .959507265 = 9.109766916. Therefore, the geometric mean of 7, 9, and 12 is9.11.
QuestionWhat is the geometric mean of 2, 4, 16, and 32?wikiHow ContributorCommunity AnswerTo make this trivially easy, use logarithms Base 2. Then the logarithms are 1, 2, 4, and 5. The simple average of those logarithms is 3, so the geometric mean of 2, 4, 16, and 32 is 2^3 = 8.Thanks!
QuestionHow do I find the geometric mean between two numbers?wikiHow ContributorCommunity AnswerTo find the geometric mean of two numbers, just find the product of those numbers and take the square root.Thanks!
QuestionHow do I identify average numbers geometric mean, arithmetic mean and harmonic mean?Top AnswererSee wikiHow's articles on each of those subjects.Thanks!
QuestionHow about finding the geometric mean of a fraction and a whole number, like 2/3 and 294?Top AnswererDo it the same way you do it with whole numbers.Thanks!
QuestionThe geographic mean of x-3 and 2x+8 is x+4. How do I solve for x?wikiHow ContributorCommunity AnswerSet it up as: (x-3)/(x+4) = (x+4)/(2x+8). That simplifies to: x + 4 = 2x - 6, which quickly yields x = 10.Thanks!
QuestionWhat is the geometric mean between 12 and 96?wikiHow ContributorCommunity AnswerFirst you need to find the product of your two numbers. In this case 12 multiplied by 96 = 1152. Then you want to find the nth root of the product (as there are only two numbers, the nth root is the square root of the product). Hence you square root 1152 and this produces the geometric mean of 12 and 96, which is 33.9 (3s.f.)Thanks!
QuestionWhat's the geometric means of 13.58, 0, 12.50, 23.80?Top AnswererThat is not a geometric sequence. Thus, there is no geometric mean.Thanks!
QuestionHow do I insert one geometric mean between 81 and 100?Top AnswererMultiply 81 by 100, then find the square root of the product. Here 81 x 100 = 8,100. The square root of 8,100 is 90.Thanks!
QuestionCan I have a geometric mean for one value?Top AnswererNo, there must be at least two numbers.Thanks!
QuestionHow do I know what geometric means are?Top AnswererA geometric mean is a "geometric average," situated between a smaller number and a larger number such that the smaller number can be multiplied by a given number to attain the geometric mean, and the geometric mean can be multiplied by that same given number to attain the larger number. The geometric mean is the square root of the product of the smaller and larger numbers.Thanks!
What are some examples of calculations of the geometric mean of return?
To calculate the geometric mean of 2 numbers, multiply those 2 numbers together, then calculate the square root of the resulting product. If you have 3 or more numbers, multiply all of the numbers together, then raise them to the power of 1 divided by n, where n is the total number of entries in the data set.
- Difference between arithmetic and geometric mean:
- If you wanted thearithmetic meanof 3, 4 and 18, for example, you would add 3 + 4 + 18, then divide by 3 because there are three numbers. The result would be 25/3 or about 8.333..., which shows that if you had three values of 8.3333..., it would give the same total as the individual values of 3, 4, and 18. The arithmetic mean answers the question, "If all the quantities had the same value, what would that value have to be in order to add up to the same total?"
- By contrast, thegeometric meananswers the question, "If all the quantities had the same value, what would that value have to be in order to have the same product when multiplied?" So to find the geometric mean of 3, 4 and 18, we would multiply 3 x 4 x 18. This would give us 216. We would then take the cubic root (cubic root because there were three original numbers). The answer would be 6. In other words, since 6 x 6 x 6 = 3 x 4 x 18, 6 is the geometric mean of 3, 4 and 18.
- The geometric mean only applies to non-negative numbers. In word problems where using a geometric mean is appropriate, the scenario will usually not make sense with negative numbers.
- The geometric mean of any set of numbers is always less than or equal to the arithmetic mean of that set. See wikipedia:AM-GM_inequality
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Video: The Geometric Mean
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