What is geometric mean in statistics?
A geometric mean is a type of average, defined as the nth positive root of the product of the terms of the data set.
Formula of Geometric mean:
There are two different formulas to calculate the geometric mean of the given data:

In the above formula:
- X2. X3…. Xn
- “n” is the total number of terms
When “n” is very large we use the following formula:

- “Σ (log X)” is the sum of the logarithm of the values.
Advantages and disadvantages of geometric mean:
In this section, we’ll discuss some pros and cons of the term geometric mean.
Advantages of Geometric Mean:
Useful for calculating average rates of change:
Geometric mean is useful in calculating the average rate of change, such as growth rate, decay rate, or interest rate, over a period of time.
Appropriate for skewed distributions:
Geometric mean is appropriate for distributions that are skewed, or where the data are clustered around small values since outliers do not influence it.
Useful for averaging ratios:
Geometric mean is useful in situations where ratios need to be averaged, such as when calculating average stock returns.
Easy to compute:
Geometric mean is easy to calculate, as it involves taking the nth root of the product of n numbers.
Disadvantages of Geometric Mean:
Sensitive to small values:
Geometric mean is sensitive to small values, meaning that small values can have a large impact on the resulting value.
Cannot be used for negative values:
Geometric mean cannot be used for data with negative values, as it requires the calculation of a logarithm of the data.
Not appropriate for sums:
Geometric mean is not appropriate for sums, as it does not take into account the magnitudes of the individual values.
Can be misleading in some situations:
Geometric mean can be misleading in situations where some values are much larger or smaller than others.
Examples:
In this section, we’ll discuss the steps for calculating the geometric mean of ungrouped data.
Example 1:
10, 12, 18, 20, 25, 30, 35
Solution:
Step 1: Extract the data.
X = 10, 12, 18, 20, 25, 30, 35
n = 7
Step 2: Put the values in the formula.
Geometric mean = (X1 * X2 . . .* Xn)1/n
Geometric mean = (10 * 12 * 18 * 20 * 25 * 30 * 35)1/7
Geometric mean = (1134000000) 0.1429
Geometric mean = 19.6570