Q&A for How to Calculate the Geometric Mean

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  • Question
    How do I identify average numbers geometric mean, arithmetic mean and harmonic mean?
    Donagan
    Top Answerer
    See wikiHow's articles on each of those subjects.
  • Question
    What is the geometric mean of 2, 4, 16, and 32?
    Community Answer
    To 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.
  • Question
    How do I find the geometric mean of 3 and 7?
    Donagan
    Top Answerer
    3 x 7 = 21. √21 = 4.58.
  • Question
    How do I find the geometric mean between two numbers?
    Community Answer
    To find the geometric mean of two numbers, just find the product of those numbers and take the square root.
  • Question
    What is the geometric mean between 12 and 96?
    Community Answer
    First 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.)
  • Question
    The geographic mean of x-3 and 2x+8 is x+4. How do I solve for x?
    Community Answer
    Set it up as: (x-3)/(x+4) = (x+4)/(2x+8). That simplifies to: x + 4 = 2x - 6, which quickly yields x = 10.
  • Question
    How about finding the geometric mean of a fraction and a whole number, like 2/3 and 294?
    Donagan
    Top Answerer
    Do it the same way you do it with whole numbers.
  • Question
    Can I have a geometric mean for one value?
    Donagan
    Top Answerer
    No, there must be at least two numbers.
  • Question
    How do I insert one geometric mean between 81 and 100?
    Donagan
    Top Answerer
    Multiply 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.
  • Question
    How do I calculate geometric mean with dates?
    Donagan
    Top Answerer
    The geometric mean concept is not applicable to calendar dates.
  • Question
    How do I know what geometric means are?
    Donagan
    Top Answerer
    A 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.
  • Question
    What is the geometric mean of 7, 1/2 and 120?
    Community Answer
    (7)(1/2)(120) = 420. Then use a calculator to find the cube root of 420, which is 7.4888.
  • Question
    What is the geometric mean of 7, 21, and 34?
    I_l1ke_gam3s
    Community Answer
    Multiply 7 by 21 by 34. That's 4,998. Then take the cube root of 4,998, because there are three numbers in the data set. The answer is approximately 17.097.
  • Question
    What is the geometric mean of 0.320, 0.150, 0.250, 0.345 and 0.145?
    I_l1ke_gam3s
    Community Answer
    Multiply all those numbers together. Then find the fifth root of the product to get the answer.
  • Question
    What is the geometric mean of 2, 3 and 4?
    I_l1ke_gam3s
    Community Answer
    Multiply 2 by 3 by 4. You get 24. Then take the cube root of 24. That's approximately 2.88.
  • Question
    What is the geometric mean of 1,4,16,64 and 256?
    I_l1ke_gam3s
    Community Answer
    This becomes 64 x 64 x 256, or 1,048,576. There are five numbers in the data set, so you take the fifth root of 1,048,576, to end up with a geometric mean of 16.
  • Question
    What is the geometric mean of 6 and 48?
    I_l1ke_gam3s
    Community Answer
    Multiply 6 by 48: you get 288. Then take the square root of 288. The geometric mean is approximately 17.
  • Question
    50,67,39,40,36,60,54,43: what is the geometric mean by a shortcut method?
    Community Answer
    There is no shortcut method. Use a scientific calculator to multiply the numbers together and then take the eighth root of that product (since there are eight numbers in the set.)
  • Question
    What is the value of 3√3000?
    Community Answer
    3√3000 = 3√[(30)(100)] = (3)(10)√30 = 30√30. You can leave the answer in that form, or you can further evaluate it: (30)(5.477) = 164.31.
  • Question
    If the geometric mean of a and x is 12, what is x?
    Community Answer
    That means the square root of ax = 12, so ax = 144. Then x = 144 / a. (You can't find a numeric value for x, because you've been given a single equation in two variables.)
  • Question
    How do I calculate the geometric mean of 87,100,41,33,65 and 84?
    Community Answer
    Multiply those six numbers together. Then use a scientific calculator or a computer program to find the sixth root of the product.
  • Question
    What is the geometric mean of 260,150,165, 201, 212, 243, 219, 227, 210, and 240?
    Community Answer
    You'll need a scientific calculator or a program that can find the nth root of a number. In this case you would multiply these numbers together and then find the tenth root of the product (because there are ten data points).
  • Question
    What is the geometric mean of 3 and 8?
    Community Answer
    (3)(8) = 24. √24 = √[(4)(6)] = 2√6. That's the best (most accurate) answer, but you can further evaluate it to (2)(2.45) = 4.9.
  • Question
    What is the geometric mean of 3 and 108?
    Community Answer
    (3)(108) = 324. The geometric mean is the square root of 324, which is18.
  • Question
    What is the geometric mean of 1,3,1,5 and 2?
    I_l1ke_gam3s
    Community Answer
    (1)(3)(1)(5)(2) = 30. Because there are five numbers, take the fifth root of 30 to get the answer, which is 1.974.
  • Question
    What is the geometric mean of 6, 3 and 2?
    I_l1ke_gam3s
    Community Answer
    (6)(3)(2) = 36. Then find the cube root of 36, because there are three numbers in the data set. The cube root of 36 is approximately 3.3.
  • Question
    Why is 8 the geometric mean of 2, 4, 16, 32?
    Donagan
    Top Answerer
    Multiply those four numbers together to get 4,096. Find the fourth root of 4,096. The fourth root is the square root of the square root, so use a calculator to find to find the square root twice. That gives you 8.
  • Question
    What's the geometric means of 13.58, 0, 12.50, 23.80?
    Community Answer
    Because zero is one of the numbers, and because you would multiply the other numbers by zero, the geometric mean is automatically zero.
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