how can you find the geometric mean?
http://www.mathsisfun.com/numbers/geometric-mean.html
thanks
To find the geometric mean, follow these steps:
1. Understand what a geometric mean is: The geometric mean is the average of a set of numbers calculated by multiplying them together, and then taking the nth root of the product, where "n" is the total number of values in the set.
2. Identify the set of numbers: Determine the set of numbers for which you want to find the geometric mean. Let's say you have "n" numbers: a₁, a₂, a₃, ..., aₙ.
3. Multiply the numbers together: Multiply all the numbers in the set together. The product would be P = a₁ * a₂ * a₃ * ... * aₙ.
4. Take the nth root of the product: Calculate the nth root of the product obtained in step 3. Since there are "n" numbers in the set, you will take the n-th root. The formula for the geometric mean is calculated as: GM = (P)^(1/n).
5. Calculate the result: Evaluate the value of the geometric mean using the calculated formula in step 4. The result will be the geometric mean of the given set of numbers.
Let's put this into practice with an example:
Example: Find the geometric mean of the numbers 2, 4, and 8.
1. Understand what a geometric mean is: The geometric mean is the average of a set of numbers calculated by multiplying them together and then taking the nth root of the product.
2. Identify the set of numbers: In this example, the set of numbers is 2, 4, and 8.
3. Multiply the numbers together: Multiply the numbers in the set. P = 2 * 4 * 8 = 64.
4. Take the nth root of the product: Since there are 3 numbers in the set, we take the third root. GM = 64^(1/3).
5. Calculate the result: Evaluate the expression. GM ≈ 4.
So, in this case, the geometric mean of the numbers 2, 4, and 8 is approximately 4.