The average tree height for a heavily forested area is almost impossible to fully quantify. Statistical sampling approaches can be used to obtain a reliable estimate for this attribute, but even in those approaches the size of the required sample can be prohibitive, both in terms of time commitment and expense. Fortunately, the height of a tree is highly correlated with the more readily available diameter of the tree at breast height. This feature can be used quite effectively in conjunction with an RSS approach to reduce the number of trees for which we must obtain the actual tree height measurement in order to obtain a reliable estimate of the average tree height in the entire forest.

Platt, Evans, and Rathbun (1988) studied the composition and dynamics of an old-growth longleaf pine population on the Wade Tract in southern Thomas County, Georgia. They obtained a variety of measurements for the longleaf pine trees in this population. In Table 15.6, we present the full height in feet and the diameter at breast height in centimeters for 396 of the trees in their study.

Using the easily measured tree diameter at breast height as the auxiliary ranking variable and a set size of k = 6, obtain an RSS (without replacement in the sampling process) of size n = 24 trees from this population of 396 trees. Estimate the average tree height of the entire population of 396 trees using the measured heights for the 24 trees in the RSS.