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.
In this section, we’ll discuss the steps for calculating the geometric mean of ungrouped data.
10, 12, 18, 20, 25, 30, 35
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