3.32 Transforming data: counting seeds. Table 3.5 shows data on the mean number of seeds produced in a year by several common tree species and the mean weight (in milligrams) of the seeds produced. (Some species appear twice because their seeds were counted in two locations.) We might expect that trees with heavy seeds would produce fewer seeds, but what is the actual form of the relationship?20 TABLE 3.5 Count and weight of seeds produced by common tree species Tree species Seed count Seed weight (mg) Tree species Seed count Seed weight (mg)
Paper birch 27,239 0.6 American beech 463 247 Yellow birch 12,158 1.6 American beech 1,892 247 White spruce 7,202 2.0 Black oak 93 1,851 Engelmann spruce 3,671 3.3 Scarlet oak 525 1,930 Red spruce 5,051 3.4 Red oak 411 2,475 Tulip tree 13,509 9.1 Red oak 253 2,475 Ponderosa pine 2,667 37.7 Pignut hickory 40 3,423 White fir 5,196 40.0 White oak 184 3,669 Sugar maple 1,751 48.0 Chestnut oak 107 4,535 Sugar pine 1,159 216.0

a. Make a scatterplot showing how the weight of tree seeds helps explain how many seeds the tree produces. Describe the form, direction, and strength of the relationship.

b. When dealing with sizes and counts, the logarithms of the original data are often a better choice of variable. Use your calculator or software to obtain the logarithms of both the seed weights and the seed counts in Table 3.5. Make a new scatterplot using these new variables. What are the form, direction, and strength of the relationship appearing in this new scatterplot? Most software programs provide the option of using logarithm scales for the axes of scatterplots, allowing you to skip the conversion to logarithms of the original data.