Calculate geometric mean how to#

How do we know which mean is correct?īecause they are averages, multiplying the original number of flies with the mean percentage change 3 times should give us the correct final population value for the correct mean. The arithmetic mean population growth factor is 4.18, while the geometric mean growth factor is 4.05. To find the arithmetic mean, add up all values and divide this number by n. You add 100 to each value to factor in the original amount, and divide each value by 100. Dayįirst, you convert percentage change into decimals. The growth factor includes the original value (100%), so to convert percentage increase into a growth factor, add 100 to each percentage increase and divide by 100. You begin with 2 fruit flies, and every 12 days you measure the percentage increase in the population.Įach percentage change value is also converted into a growth factor that is in decimals. You’re interested in understanding how environmental factors change these rates. The geometric mean is more accurate than the arithmetic mean for showing percentage change over time or compound interest.įor example, say you study fruit fly population growth rates. The geometric mean is more accurate here because the arithmetic mean is skewed towards values that are higher than most of your dataset. While the arithmetic means show higher efficiency for Machine B, the geometric means show that Machine B is more efficient.

Now you compare machine efficiency using arithmetic and geometric means. To find the mean efficiency of each machine, you find the geometric and arithmetic means of their procedure rating scores. You compare the efficiency of two machines for three procedures that are assessed on different scales. Example: Geometric mean of widely varying values The average voter turnout of the past five US elections was 54.64%. Step 2: Find the nth root of the product ( n is the number of values). Step 1: Multiply all values together to get their product. You’re interested in the average voter turnout of the past five US elections.

Calculate geometric mean how to#

We’ll walk you through some examples showing how to find the geometric means of different types of data. While the arithmetic mean is appropriate for values that are independent from each other (e.g., test scores), the geometric mean is more appropriate for dependent values, percentages, fractions, or widely ranging data. Because these types of data are expressed as fractions, the geometric mean is more accurate for them than the arithmetic mean. The geometric mean is best for reporting average inflation, percentage change, and growth rates.

If any value in the dataset is zero, the geometric mean is zero.

The geometric mean can only be found for positive values.

Find the nth root of the product ( n is the number of values).īefore calculating this measure of central tendency, note that:.

Multiply all values together to get their product.

There are two main steps to calculating the geometric mean: See editing example Calculating the geometric mean These formulas are equivalent because of the laws of exponents: taking the nth root of x is exactly the same as raising x to the power of 1/ n.

In the second formula, the geometric mean is the product of all values raised to the power of the reciprocal of n. In the first formula, the geometric mean is the nth root of the product of all values. The symbol pi ( ) is similar to the summation sign sigma (Σ), but instead it tells you to find the product of what follows after it by multiplying them all together.

The geometric mean formula can be written in two ways, but they are equivalent mathematically.

You can calculate the geometric mean by hand or with the help of our geometric mean calculator below.

Frequently asked questions about central tendency.

When is the geometric mean better than the arithmetic mean?.

Example: Geometric mean of widely varying values.

When should you use the geometric mean?.