The arithmetic mean is one of the most commonly used statistics. The choice of the mean then depends upon the statistical properties of the. A KNOWLEDGE STRUCTURE FOR THE ARITHMETIC MEAN. The properties that make the arithmetic mean useful are that the numbers to the left of the. In statistics there is no difference between the mean and average Two other terms median and mode are used to describe different approaches for finding a. The population mean is an average of a group characteristic The group could be a person item or thing like all the people living in the United.