Different varieties of the bright tropical flower Heliconia are fertilized by different species of hummingbirds. Over time, the lengths of the flowers and the form of the hummingbirds’ beaks have evolved to match each other. Below are data on the lengths in millimeters of two varieties of these flowers on the island of Dominica. Exercises 65-69 use these data.

238

Heliconia caribaea Red
37.40 38.07 38.87 40.66 41.93
37.78 38.10 39.16 41.47 42.01
37.87 38.20 39.63 41.69 42.18
37.97 38.23 39.78 41.90 43.09
38.01 38.79 40.57
Heliconia caribaea Yellow
34.57 35.45 36.03 36.66 37.02
34.63 35.68 36.11 36.78 37.10
35.17 36.03 36.52 36.82 38.13
Table 5.46: Thanks to Ethan J. Temeles of Amherst College for providing the data. His work is described in Ethan J. Temeles and W. John Kress, Adaptation in a plant-hummingbird association, Science, 300 (2003): 630-633.

Question 5.97

67. The biologists who collected the flower length data compared the two Heliconia varieties using statistical methods based on the mean and standard deviation.

  1. Find and for each variety.
  2. Based on Exercise 65, which distribution is more suitable for use of and as summaries? Why?

67.

(a) Red: , ; yellow: ,

(b) The mean and standard deviation are better suited to the symmetrical yellow distribution.