Geometric Mean
The geometric mean is the mathematical average of a set of products, the calculation of which is commonly used to determine the performance results of an investment or portfolio. It is technically defined as "the nth root product of n numbers." where we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers), etc.
The geometric mean very useful when working with percentages, which are derived from values, while the standard arithmetic means works with the values themselves.
The geometric mean is an important method for calculating portfolio performance for various reasons, but one of the most significant is it takes into account the effects of compounding
Geometric mean formula
How to calculate Geometric mean
Example: Calculate the Geometric Mean of 3 and 27?
First we multiply them: 3 × 27 = 81
Then (as there are two numbers) take the square root: √81 = 9
In one line:
Geometric Mean of 3 and 27 = √(3 × 27) = 9
It is like the area is the same!
Example: What is the Geometric Mean of 16, 51.2 and 5?
First we multiply them: 16 × 51.2 × 5 = 4096
Then (as there are three values) take the cube root: 3√4096 = 16
In one line:
Geometric Mean = 3√(16 × 51.2 × 5) = 16
It is like the volume is the same:
Example: Calculate the Geometric Mean of 81, 27, 9, 3 and 1?
First we multiply them: 81 × 27 × 9 × 3 × 1 = 59049
Then (as there are five numbers) take the 5th root: 5√59049 = 9
In one line:
Geometric Mean = 5√(81 × 27 × 9 × 3 × 1) = 9
I can't show you a nice picture of this, but it is still true that:
1 × 3 × 9 × 27 × 81 = 9 × 9 × 9 × 9 × 9
Use of Geometric Mean
The Geometric Mean is very useful when we want to compare things with very different properties.
Example: you want to buy a new camera.
One camera has a zoom of 210 and gets an 8 in reviews,
The other has a zoom of 260 and gets a 6 in reviews.
Comparing using the usual arithmetic mean gives (210+8)/2 = 109 vs (260+6)/2 = 133. The zoom of camera is such a big number that the user rating gets lost.
But when you Calculate the geometric means of the two cameras are:
√(210 × 8) = 40.98..
√(260 × 6) = 39.496..
So, even though the zoom is 50 bigger, the lower user rating of 6 is still important.
Geometric mean in Hindi
In this video I have explained how to calculate geometric mean with examples.
So please watch the full video for the clear explanation.
Geometric mean
geometric mean formula
geometric mean in hindi
how to find geometric mean
geometric mean in statistics
0 Comments