Definition of the word arithmetic mean

The term "arithmetic mean" or simply "average" derives from the Greek word "arithmos," which means "number," and the Latin word "medianus," meaning "of the middle." When Navier, a French mathematician, introduced the term "mean proportional" in the early 19th century to describe a value that falls in the middle of a set of proportions, it didn't become widely used. The term "arithmetic mean" was popularized by another mathematician of that era, blue-blooded British polymath Charles Babbage, who defined it as the value obtained by adding up all the numbers in a set and dividing by the number of values. This definition came into use commonly in the mid-19th century, after Victor Cousin, a French philosopher, used it while teaching composite proportions to his students. The term "mean" as used to describe it, however, is thought to have been independently popularized by another British mathematician, Water Whedstone. The use of the word "arithmetic" is meant to highlight the fact that the calculation of an arithmetic mean is a straightforward arithmetic operation that involves no complex algebraic functionalities like logarithms, roots, or exponents. The term "average" is often used in place of "arithmetic mean" due to its more straightforward and commonly used nature, but it can lead to misunderstandings with other statistical concepts like median and mode.