• Source: 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





{\displaystyle {\sqrt {\frac {\sum {D_{i}}^{2}}{n}}}}


where





D

i





{\displaystyle {D_{i}}}

is the diameter at breast height of the ith 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






{\displaystyle {\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=0.00007854.




References

Kata Kunci Pencarian:

• Quadratic mean diameter
• Mean
• Stand density index
• AM–GM inequality
• QM-AM-GM-HM inequalities
• Geometric mean
• Stand density management diagram
• Arithmetic mean
• Conic section
• Forest inventory