The trees data from the R datasets package:

This data set provides measurements of the girth, height and volume of timber in 31 felled black cherry trees. Note that girth is the diameter of the tree (in inches) measured at 4 ft 6 in above the ground.

The correlation between girth & height is $0.52$, while the ratio of the standard deviations of girth to height is only $\frac{3.14''}{76.4''}=0.04$.

It's rather common to measure correlations between measurements of large magnitude to measurements of small magnitude with roughly similar coefficients of variation, & there's no particular reason such correlations should be small.

Note that if girth were expressed as circumference rather than diameter the ratio of standard deviations would be 0.13; in fact some queer way of expressing the observations might always be found to raise the value of the ratio over that of the correlation.

The trees data from the R datasets package:

This data set provides measurements of the girth, height and volume of timber in 31 felled black cherry trees. Note that girth is the diameter of the tree (in inches) measured at 4 ft 6 in above the ground.

The correlation between girth & height is $0.52$, while the ratio of the standard deviations of girth to height is only $\frac{3.14''}{76.4''}=0.04$.

It's rather common to measure correlations between measurements of large magnitude to measurements of small magnitude with roughly similar coefficients of variation, & there's no particular reason such correlations should be small.

Note that if girth were expressed as circumference rather than diameter the ratio of standard deviations would be 0.13; in fact some queer way of expressing the observations might always be found to raise the value of the ratio over that of the correlation. So the question's about not just what's likely to be observed, but what's likely to be written down.

The trees data from the R datasets package:

This data set provides measurements of the girth, height and volume of timber in 31 felled black cherry trees. Note that girth is the diameter of the tree (in inches) measured at 4 ft 6 in above the ground.

The correlation between girth & height is $0.52$, while the ratio of the standard deviations of girth to height is only $\frac{3.14''}{76.4''}=0.04$.

It's rather common to measure correlations between measurements of large magnitude to measurements of small magnitude with roughly similar coefficients of variation, & there's no particular reason such correlations should be small.

The trees data from the R datasets package:

This data set provides measurements of the girth, height and volume of timber in 31 felled black cherry trees. Note that girth is the diameter of the tree (in inches) measured at 4 ft 6 in above the ground.

The correlation between girth & height is $0.52$, while the ratio of the standard deviations of girth to height is only $\frac{3.14''}{76.4''}=0.04$.

It's rather common to measure correlations between measurements of large magnitude to measurements of small magnitude with roughly similar coefficients of variation, & there's no particular reason such correlations should be small.

Note that if girth were expressed as circumference rather than diameter the ratio of standard deviations would be 0.13; in fact some queer way of expressing the observations might always be found to raise the value of the ratio over that of the correlation.