Quadratic mean diameter

In forestry, quadratic mean diameter or QMD is a measure of Central tendency which is considered more appropriate than arithmetic mean for characterizing the group of trees which have been measured. For n trees, QMD is calculated using the quadratic mean formula:

∑ D i 2 n

where D i is the diameter at breast height of the i^th tree. Compared to the arithmetic mean, QMD assigns greater weight to larger trees - QMD is always greater than or equal to arithmetic mean for a given set of trees. QMD can be used in timber cruises to estimate the standing volume of timber in a forest, because it has the practical advantage of being directly related to Basal area, which in turn is directly related to volume. QMD can also be calculated as:

B A k ∗ n

where BA is stand basal area, n is the number of trees, and k is a constant based on measurement units - for BA in ft² and DBH in inches, k=0.005454; for BA in m² and DBH in cm, k=0.0000785.