Describing Data on a Single Variable: Measures of Central Tendency

blood pressure readings less than 127 mm Hg were then classified according to their serum cholesterol level. Serum Cholesterol mg100cc Frequency 0.0 –199.9 119 200.0 –219.9 88 220.0 –259.9 127 greater than 259 74 a. Estimate the mode, median, and mean for the serum cholesterol readings if possible. b. Which of the three summary statistics is more informative concerning a typical serum cholesterol level for the group of men? Explain your answer. Env. 3.21 The ratio of DDE related to DDT to PCB concentrations in bird eggs has been shown to have had a number of biological implications. The ratio is used as an indication of the move- ment of contamination through the food chain. The paper “The ratio of DDE to PCB concentra- tions in Great Lakes herring gull eggs and its use in interpreting contaminants data’’ [Journal of Great Lakes Research 1998 241:12 –31] reports the following ratios for eggs collected at 13 study sites from the five Great Lakes. The eggs were collected from both terrestrial- and aquatic-feeding birds. DDE to PCB Ratio Terrestrial Feeders 76.50 6.03 3.51 9.96 4.24 7.74 9.54 41.70 1.84 2.50 1.54 Aquatic Feeders 0.27 0.61 0.54 0.14 0.63 0.23 0.56 0.48 0.16 0.18 a. Compute the mean and median for the 21 ratios, ignoring the type of feeder. b. Compute the mean and median separately for each type of feeder.

c. Using your results from parts a and b, comment on the relative sensitivity of the

mean and median to extreme values in a data set.

d. Which measure, mean or median, would you recommend as the most appropriate

measure of the DDE to PCB level for both types of feeders? Explain your answer. Med. 3.22 A study of the survival times, in days, of skin grafts on burn patients was examined in Woolson and Lachenbruch [Biometrika 1980 67:597– 606]. Two of the patients left the study prior to the failure of their grafts. The survival time for these individuals is some number greater than the reported value. Survival time days: 37, 19, 57, 93, 16, 22, 20, 18, 63, 29, 60 The “’’ indicates that the patient left the study prior to failure of the graft; values given are for the day the patient left the study. a. Calculate the measures of center if possible for the 11 patients. b. If the survival times of the two patients who left the study were obtained, how would these new values change the values of the summary statistics calculated in a? Engin. 3.23 A study of the reliability of diesel engines was conducted on 14 engines. The engines were run in a test laboratory. The time in days until the engine failed is given here. The study was terminated after 300 days. For those engines that did not fail during the study period, an asterisk is placed by the number 300. Thus, for these engines, the time to failure is some value greater than 300. Failure time days: 130, 67, 300, 234, 90, 256, 87, 120, 201, 178, 300, 106, 289, 74 a. Calculate the measures of center for the 14 engines. b. What are the implications of computing the measures of center when some of the exact failure times are not known?