Geometric mean allows you to find the mean value of a set of data, but instead of adding the values and dividing them as you would for the arithmetic mean, you need to multiply them before calculating the root. You can use the geometric mean to calculate the average return on an investment or to show how much a value has grown over a specific period. To find it, multiply all the numbers in the set before extracting the nth root, where n equals the total number of data in the set. If you prefer, you can get the geometric mean using your calculator's logarithmic function.
Steps
Method 1 of 2: Finding the Geometric Mean of a Data Set
Step 1. Multiply the values you want to get the geometric mean
You can do this manually or using a calculator. Multiply all the numbers in the set you are considering to find their product. Write the result so you don't forget it.
- For example, if the set of values is 3, 5, and 12, you would write: (3 x 5 x 12) = 180.
- In another example, if you want to get the geometric mean of the numbers 2 and 18, write: (2 x 18) = 36.
Step 2. Find the nth root of the product where n is the number of data
To obtain n, count how many values are present in the set of which you are calculating the geometric mean. Use n to determine what root you need to calculate of the product. For example, for two values it calculates the square root, the cubic root for three numbers, and so on. Solve the equation with the calculator and write the result.
- For example, for the set 3, 5, and 12, write: ∛ (180) ≈ 5, 65.
- In the second example, with 2 and 18, write: √ (36) = 6.
Variant:
you can also write the value as a 1 / n exponent if it is easier to enter it into your calculator. For example, for the set 3, 5, and 12, you can write (180)1/3 instead of ∛ (180).
Step 3. Convert percentages to decimal equivalents
If there are percentage increases or decreases in the dataset, avoid using percentage values for the geometric mean calculation, otherwise you will get an incorrect result. If the variation is an increment, move the comma two digits to the left and add 1. If the variation is a reduction, move the comma two digits to the left and subtract from 1.
- For example, imagine you want to calculate the geometric mean of an object's value that increases by 10%, then falls by 3%.
- Convert 10% to a decimal number, then add it to 1 to get 1, 10.
- Convert 3% to a decimal number and subtract it from 1 to get 0.97.
- Use the two decimal values to find the geometric mean: √ (1, 10 x 0, 97) ≈ 1, 03.
- Convert the number back to a percentage by moving the comma two digits to the right and subtracting 1 to find an overall increase of 3%.
Method 2 of 2: Calculate the Geometric Mean with Logarithms
Step 1. Add the logarithmic values of each number in the collection
The LOG function takes a base 10 value and determines how many times you need to raise it to a power of 10 to get to that value. Find the LOG function on the calculator, which is usually on the left side. Press the LOG button and enter the first number of the set. Write "+" before pressing LOG for the second value. Continue separating the LOG functions of each value with the plus sign before calculating the sum.
- For example, with the set 7, 9 and 12, you would write log (7) + log (9) + log (12) before pressing "=" on the calculator. Once the function is solved, the sum will be approximately 2.878521796.
- If you prefer, you can calculate each logarithm separately before adding them together.
Step 2. Divide the sum of the logarithmic values by the number of data in the set
Count the number of values in the set you are considering, then use it to divide the sum you calculated. The result will be the logarithmic value of the geometric mean.
In our example, the set consists of 3 numbers, so write: 2, 878521796/3 ≈ 0, 959507265
Step 3. Calculate the antilogarithm of the quotient to obtain the geometric mean
The antilogarithm function is the inverse of the LOG function of your calculator and converts the value back to base 10. Look for the symbol "10x"on your calculator, which is usually a secondary function of the LOG button. To activate the antilogarithm, press the" 2nd "key in the upper left corner of the calculator, followed by the LOG key. Type the quotient you calculated into the last step before solving the equation.
In our example, on the calculator you have to write: 10(0, 959507265) ≈ 9, 11.
Advice
- It is not possible to calculate the geometric mean of negative numbers.
- All sets containing the value 0 have a geometric mean of 0.
