Comparison of the Arithmetic and Geometric Means in Estimating Crown Diameter and Crown Cross-Sectional Area

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Abstract:

The use of the geometric and arithmetic means for estimating tree crown diameter and crown cross-sectional area were examined for trees with crown width measurements taken at the widest point of the crown and perpendicular to the widest point of the crown. The average difference between the geometric and arithmetic mean crown diameters was less than 0.2 ft in absolute value. The mean difference between crown cross-sectional areas based on the geometric and arithmetic mean crown diameters was less than 6.0 ft2 in absolute value. At the plot level, the average difference between cumulative crown cross-sectional areas based on the geometric and arithmetic mean crown diameters amounted to less than 2.5% of the total plot area. The practical significance of these differences will depend on the final application in which the mean crown diameters are used.

Keywords: AM‐GM inequality; crown width; eccentricity; forest inventory

Document Type: Technical Note

Publication date: November 1, 2010

More about this publication?
  • Each regional journal of applied forestry focuses on research, practice, and techniques targeted to foresters and allied professionals in specific regions of the United States and Canada. The Southern Journal of Applied Forestry covers an area from Virginia and Kentucky south to as far west as Oklahoma and east Texas.
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