For any two positive numbers a and b, the geometric mean of a and b is the positive number x such that . Corollary 1: The length of the altitude of the hypotenuse of a right triangle is the geometric mean of the lengths of the sub-segments of the hypotenuse. Corollary 2: The altitude of the hypotenuse of a right triangle intersects it so that the length of each leg is the geometric mean of the length of its adjacent segment of the hypotenuse and the length of the entire hypotenuse.

The th root of the product of observations or predictions of a quantity.

If a, b, and x are positive numbers with a\x=x\b, then x is the geometric mean between a and b.

the mean of n numbers expressed as the n-th root of their product

a type of statistical average that minimises the effects of both high and low values

A measure of the central tendency of a data set that minimizes the effects of extreme values.

The antilog (base 10) of the arithmetic mean of the sample result logarithm (base 10). (3)

The nth root of the product of n values.

The appropriate measure of central tendency on a multiply-divide scale. On the Standard Celeration Chart you derive a geometric mean by multiplying N number of frequencies and then taking the Nth root of that.

Square root of the sum of the squares.

a type of average (measure of central tendency), which is defined as the "-th" root of the product of all the values in a set of numerical data (where = # of values in the data set)

A method of estimating an overall mean (or average) from a group of subsamples, that is resistant to the presence of a small number of very high values. The number of CFUs (see above) in swimming waters can range from nil to millions over a reporting period, so it is difficult to determine a representative value. The geometric mean is calculated from the average of log-transformed data, which discounts the influence of very large values.

The geometric mean of 'n' fecal coliform samples is the nth root of their product. For example, the geometric mean of 5 values is the 5th root of the product of the 5 values.

The th root of the product of terms.

The square root of the product of two numbers. It is also called the mean proportional.

For positive numbers, the positive th root of their product; that is, for the set of positive numbers , the geometric mean is the quantity (). Compare arithmetic mean.

The geometric mean of a set of positive data is defined as the nth root of the product of all the members of the set, where n is the number of members.