arithmetic mean vs. geometric mean

Question

What is the difference between the arithmetic mean and the geometric mean related to statistical analysis of a data set? I'm working on analyzing a data set involving height measurements. My professor is using the "geometric mean" for the calculated percentiles of height-for-age and adding 1 to each of the values of height-for-age percentile for each subject. However, he's not adding 1 to the other measures related to height such as height-for-age z-score, or height in cm. 

 

Thanks for your help.

 

Patricia Bryan

Answer 1

The arithmetic mean is the average of 2 or more numbers.

 

The arithmetic mean of x and y is:  (x + y)/2.

 

The geometric mean is the square root of the product of two numbers.

 

For example:  the geometric mean of 4 and 9 is 6, the square root of 4*9.

 

This comes from the following equation:  9/x = x/4,  the x's being the means and the 9 and 4 being the extremes.