forestry Forestry is the science and craft of creating, managing, planting, using, conserving and repairing forests, woodlands, and associated resources for human and environmental benefits. Forestry is practiced in plantations and natural stands. Th ...

, quadratic mean diameter or QMD is a measure of

central tendency In statistics, a central tendency (or measure of central tendency) is a central or typical value for a probability distribution.Weisberg H.F (1992) ''Central Tendency and Variability'', Sage University Paper Series on Quantitative Applications ...

which is considered more appropriate than

arithmetic mean In mathematics and statistics, the arithmetic mean ( ) or arithmetic average, or just the ''mean'' or the ''average'' (when the context is clear), is the sum of a collection of numbers divided by the count of numbers in the collection. The colle ...

for characterizing the group of trees which have been measured. For ''n'' trees, QMD is calculated using the

quadratic mean In mathematics and its applications, the root mean square of a set of numbers x_i (abbreviated as RMS, or rms and denoted in formulas as either x_\mathrm or \mathrm_x) is defined as the square root of the mean square (the arithmetic mean of the ...

formula:

\sqrt

where

is the

diameter at breast height Diameter at breast height, or DBH, is a standard method of expressing the diameter of the trunk or bole of a standing tree. DBH is one of the most common dendrometric measurements. Tree trunks are measured at the height of an adult's breast, ...

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 cruise Forest inventory is the systematic collection of data and forest information for assessment or analysis. An estimate of the value and possible uses of timber is an important part of the broader information required to sustain ecosystems. When taki ...

s to estimate the standing volume of timber in a forest, because it has the practical advantage of being directly related to

basal area Basal area is the cross-sectional area of trees at breast height (1.3m or 4.5 ft above ground). It is a common way to describe stand density. In forest management, basal area usually refers to merchantable timber and is given on a per hectar ...

, which in turn is directly related to volume. QMD can also be calculated as:

\sqrt

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=0.00007854.

References

{{Reflist Forest modelling