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 as:

$\sqrt {\frac{\sum{D_i}^{2}}{n}}$

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. ^[1] QMD can also be calculated as:

$\sqrt {\frac{BA}{k * n}}$

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.

References

1. Curtis, Robert O.; Marshall, David D. (2000), "Why quadratic mean diameter?" (PDF), Western Journal of Applied Forestry 15 (3): 137–139, retrieved 2012-06-13