Cheek teeth of extinct primates. Refer to the American Journal of Physical Anthropology (Vol. 142, 2010) study of the characteristics of cheek teeth (e.g., molars) in an extinct primate species, Exercise 2.65 (p. 90). The data on dentary depth of molars (in millimeters) for 18 cheek teeth extracted from skulls are reproduced in the table.

Data on Dentary Depth (mm) of Molars 18.12 15.76 13.25 19.48 17.00 16.12 19.36 13.96 18.13 15.94 16.55 14.02 15.83 15.70 14.04 19.70 17.83 16.20 Based on Boyer, D. M., Evans, A. R., and Jernvall, J. “Evidence of dietary differentiation among late Paleocene–early Eocene Plesiadapids (Mammalia, primates),” American Journal of Physical Anthropology, Vol. 142, 2010 (Table A3).

a. Find the range of the data set. If the largest depth measurement in the sample were doubled, how would the range change? Would it increase or decrease?

b. Find the variance of the data set. If the largest depth measurement in the sample were doubled, how would the variance change? Would it increase or decrease?

c. Find the standard deviation of the data set. If the largest depth measurement in the sample were doubled, how would the standard deviation change? Would it increase or decrease?