In order to calculate Geometric Mean we multiply the given numbers altogether and then take a square root given that there are two numbers or cube root for three numbers 5th root for five numbers etc. The place that a geometric mean is most often used and therefore a geometric standard deviation is when calculating investment returns over time especially when the returns involve compound interest. Given two aspect ratios the geometric mean of them provides a compromise between them distorting or cropping both in some sense equally.
How you calculate the geometric mean is rather easy-you use the GEOMEAN function built into Excel.
Another way to calculate the geometric mean is with logarithms as it is also the average of logarithmic values converted back to base 10. To compute the geometric mean and geometric CV you can use the DISTLOGNORMAL option on the PROC TTEST statement as follows. This is equivalent to raising 19500 to the 15-th power. This formula tells us to multiply all the terms radicands within the radical the symbol for roots and then to find the n t h root of them where n is how many radicands you have.