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:

$\backslash sqrt\; \{\backslash frac\{\backslash sum\{D\_i\}^\{2\}\}\{n\}\}$

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.{{Citation

| title = Why quadratic mean diameter?

| url = http://www.cnr.uidaho.edu/for274new/pdfs/s6.pdf

| year = 2000

| journal = Western Journal of Applied Forestry

| pages = 137–139

| volume = 15

| issue = 3

| last1 = Curtis | first1 = Robert O.

| last2 = Marshall | first2 = David D.

| access-date = 2012-06-13}}

QMD can also be calculated as:

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

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=0.00007854.