Mean: The
arithmetical mean of a collection of n numbers is the sum of the numbers
divided by n. (n is here at least 1). In a formula: 1/n Σ_{i} (X_{i}),
where Σ_{i} (X_{i}) = X_{1} + .. + X_{n} = the sum of the individual
numbers with n the number of them. Thus the mean of
{3,4,5}=1/3.(3+4+5)=1/3.12=4.
The mean is the most common mathematical
and statistical sense of average. It is a
useful way to say something about all the members in the collection, but has
at least two disadvantages: It involves numbers, that when derived from the
properties of real things abstract from all these properties, and it produces
a number which itself may not be in the collection of which it is the mean.
(Thus, the mean human being, when limbs and appendages are counted, has
two arms, two legs, two ears, one ball and one breast, approximately. As the
reader will appreciate, this result illustrates one of the powers of
statistics.)
