Chapter 8.2, Problem LC

Various Means

When we find the mean of a set of numbers, we are attempting to find the “ middle” or “center ” of the set of numbers. The arithmetic mean that we defined in this section is used so frequently that it is hard to believe that there could be any other way to find the middle. However, there are several other ways to find the middle that produce approximately the same results. The wealth (in today's dollars) of the top five richest Americans of all time is shown in the table (Infoplease, www.infoplease.com).

Name	Wealth ($hillinns)
John D. Rockefeller	189.6
Andrew Carnegie	100.5
Cornelius Vanderbilt	95.9
John Jacob Astor	78.0
William H. Gates III	61.7

Find the median, the score for which approximately one-half of the scores are lower and one-half of the scores are higher.

Find the geometric mean, the n th root of the product of the n scores:

GM=v(n_1•x_2•x_3• ••• •x_n )

c) Find the harmonic mean, the number of scores divided by the sum of the reciprocals of the scores:

HM=n/(Σ1/x)

d) Find the quadratic mean by finding the sum of the squares of the scores, divide by n, then take the square root:

QM=v((Σx²)/n)