MEAN

In Mathematics, a quantity having an in termed i ate value between several others which are formed according to any a igned law of succe ion. The arithmetical mean of several quantities is simply the average formed by dividing the sum of sill the quantities by their number, in physical inquiries, where a great number of values of a quantity have been determined by observation or experiments, of which the error is as likely to be in exce as delect, the average or arithmetical mean is the most probable result. The geometrical mean between two quantities, or the mean proportional, is a quantity which forms the middle term of a duplicate ratio, or continued proportion of three terms: viz., such that the first given term is to the quantity sought as that quantity is to the other given term. In arithmetic, it is the square root of the product of the two given terms. The harmonical mean is such a number that, the first and third terms being given, the first is to the third as the difference of the first and second is to the difference of the second and third; or, if a, b, c be the numbers, b being the mean — 2ac 2 1,1 a-\- c b a c [s. 742]