this kind of mean, called the arithmetic mean, is just one of several possible mean. Another often-used mean is the geometric mean, defined as ad. imagine you own a rectangular plot of land and you want to build on it a square-shaped house. your plot, however, is rather long and narrow, so it doesn't provide enough space for your dream house. you therefore propose to your realtor to trade it off for a square-shaped plot of equal area. what should be the side of this square? If the length and width of the rectangle are a and b, its area is ab. setting this equal to the area of a square of side x, we get ab=x^2,or x=ab-the geometric mean of a and b. for example, the geometric of 3 and 5 is 3*5=15=3.87,a shade less than their arithmetric mean.