What is the formula of a mean?

Answer 1

Obtain the arithmetic mean of a batch of numbers by adding them up and dividing by their count. For example, the arithmetic mean of 3, 5, and 10 equals (3 + 5 + 10)/ 3 = 6. There are other kinds of means, such as geometric and harmonic, but usually when the type of mean is not specified the arithmetic mean is intended. For completeness I will also provide an answer from probability theory. The mean of a random variable is its expectation, which is defined to be its integral. If the random variable has a distribution f(x)dx, its mean equals the integral of x*f(x)dx over all real numbers. This is related to the first definition of arithmetic mean. A batch of numbers gives rise to a random variable supported at those numbers, where the probability of each number is proportional to the number of times it occurs in the batch. (This is the empirical distribution function of the batch.) The arithmetic mean of the batch equals the expectation of that random variable.