Mean 

Plain definition:  Unless you are a scientist, financial advisor or a mathematician, the mean normally refers to an arithmetic mean.   To find an artihmetic mean, add up all of the measurements and divide that sum by the number (n) of measurements. 

Here is the formula to find the (arithmetic) mean: 

AKA: average 

*Note: The mean is the most used mathematical concept in statistics, so learn it well.

**Note: the values of the mean, median and mode from a normal distribution are relatively close to each other.

Example:  Test scores (measurements) were:  45, 56, 59, 38, 48, 42, 61 and 55. 

So the (arithmetic) mean is 45 + 56 + 59 + 38 + 48 + 42 + 61 + 55 = 404   Now divide the sum (404) by the number of measurements (represented by the variable "n" - how many test scores: in this example n = 8).  So, 404 divided by 8 equals 50.5 (the arithmetic mean test score).

A geometric mean is something completely different.  Instead of adding up the measurements, you multiply them and take the nth root of the product.

Example:  Test scores (measurements) were:  45, 56, 59, 38, 48, 42, 61 and 55. 

So the (geometric) mean is 45 x 56 x 59 x 38 x 48 x 42 x 61 x 55 = 38,213,709,811,200   Now take the 8th root of that product and you get 49.9 (the geometric mean test score).

Here is the formula to find the (geometric) mean: 

Problem:  Find the (arithmetic) mean of the following test scores:
                                       75, 82, 62, 55, 95, 99, 76, 82 and 81.

                                            
                                         Video example in English

Video example in Spanish