Short Summary: Lists estimates of the percentage of body fat determined by underwater weighing and various body circumference measurements for 252 men. Classroom use of this data set: This data set can be used to illustrate multiple regression techniques. Accurate measurement of body fat is inconvenient/costly and it is desirable to have easy methods of estimating body fat that are not inconvenient/costly. More Details: A variety of popular health books suggest that the readers assess their health, at least in part, by estimating their percentage of body fat. In Bailey (1994), for instance, the reader can estimate body fat from tables using their age and various skin-fold measurements obtained by using a caliper. Other texts give predictive equations for body fat using body circumference measurements (e.g. abdominal circumference) and/or skin-fold measurements. See, for instance, Behnke and Wilmore (1974), pp. 66-67; Wilmore (1976), p. 247; or Katch and McArdle (1977), pp. 120-132). Percentage of body fat for an individual can be estimated once body density has been determined. Folks (e.g. Siri (1956)) assume that the body consists of two components - lean body tissue and fat tissue. Letting D = Body Density (gm/cm^3) A = proportion of lean body tissue B = proportion of fat tissue (A+B=1) a = density of lean body tissue (gm/cm^3) b = density of fat tissue (gm/cm^3) we have D = 1/[(A/a) + (B/b)] solving for B we find B = (1/D)*[ab/(a-b)] - [b/(a-b)]. Using the estimates a=1.10 gm/cm^3 and b=0.90 gm/cm^3 (see Katch and McArdle (1977), p. 111 or Wilmore (1976), p. 123) we come up with "Siri's equation": Percentage of Body Fat (i.e. 100*B) = 495/D - 450. Volume, and hence body density, can be accurately measured a variety of ways. The technique of underwater weighing "computes body volume as the difference between body weight measured in air and weight measured during water submersion. In other words, body volume is equal to the loss of weight in water with the appropriate temperature correction for the water's density" (Katch and McArdle (1977), p. 113). Using this technique, Body Density = WA/[(WA-WW)/c.f. - LV] where WA = Weight in air (kg) WW = Weight in water (kg) c.f. = Water correction factor (=1 at 39.2 deg F as one-gram of water occupies exactly one cm^3 at this temperature, =.997 at 76-78 deg F) LV = Residual Lung Volume (liters) (Katch and McArdle (1977), p. 115). Other methods of determining body volume are given in Behnke and Wilmore (1974), p. 22 ff. The variables listed below, from left to right, are: Density determined from underwater weighing Percent body fat from Siri's (1956) equation Age (years) Weight (lbs) Height (inches) Neck circumference (cm) Chest circumference (cm) Abdomen 2 circumference (cm) Hip circumference (cm) Thigh circumference (cm) Knee circumference (cm) Ankle circumference (cm) Biceps (extended) circumference (cm) Forearm circumference (cm) Wrist circumference (cm) (Measurement standards are apparently those listed in Benhke and Wilmore (1974), pp. 45-48 where, for instance, the abdomen 2 circumference is measured "laterally, at the level of the iliac crests, and anteriorly, at the umbilicus".) These data are used to produce the predictive equations for lean body weight given in the abstract "Generalized body composition prediction equation for men using simple measurement techniques", K.W. Penrose, A.G. Nelson, A.G. Fisher, FACSM, Human Performance Research Center, Brigham Young University, Provo, Utah 84602 as listed in _Medicine and Science in Sports and Exercise_, vol. 17, no. 2, April 1985, p. 189. (The predictive equations were obtained from the first 143 of the 252 cases that are listed below). The data were generously supplied by Dr. A. Garth Fisher who gave permission to freely distribute the data and use for non-commercial purposes. References: Bailey, Covert (1994). _Smart Exercise: Burning Fat, Getting Fit_, Houghton-Mifflin Co., Boston, pp. 179-186. Behnke, A.R. and Wilmore, J.H. (1974). _Evaluation and Regulation of Body Build and Composition_, Prentice-Hall, Englewood Cliffs, N.J. Siri, W.E. (1956), "Gross composition of the body", in _Advances in Biological and Medical Physics_, vol. IV, edited by J.H. Lawrence and C.A. Tobias, Academic Press, Inc., New York. Katch, Frank and McArdle, William (1977). _Nutrition, Weight Control, and Exercise_, Houghton Mifflin Co., Boston. Wilmore, Jack (1976). _Athletic Training and Physical Fitness: Physiological Principles of the Conditioning Process_, Allyn and Bacon, Inc., Boston. 1.0708 12.3 23 154.25 67.75 36.2 93.1 85.2 94.5 59.0 37.3 21.9 32.0 27.4 17.1 1.0853 6.1 22 173.25 72.25 38.5 93.6 83.0 98.7 58.7 37.3 23.4 30.5 28.9 18.2 1.0414 25.3 22 154.00 66.25 34.0 95.8 87.9 99.2 59.6 38.9 24.0 28.8 25.2 16.6 1.0751 10.4 26 184.75 72.25 37.4 101.8 86.4 101.2 60.1 37.3 22.8 32.4 29.4 18.2 1.0340 28.7 24 184.25 71.25 34.4 97.3 100.0 101.9 63.2 42.2 24.0 32.2 27.7 17.7 1.0502 20.9 24 210.25 74.75 39.0 104.5 94.4 107.8 66.0 42.0 25.6 35.7 30.6 18.8 1.0549 19.2 26 181.00 69.75 36.4 105.1 90.7 100.3 58.4 38.3 22.9 31.9 27.8 17.7 1.0704 12.4 25 176.00 72.50 37.8 99.6 88.5 97.1 60.0 39.4 23.2 30.5 29.0 18.8 1.0900 4.1 25 191.00 74.00 38.1 100.9 82.5 99.9 62.9 38.3 23.8 35.9 31.1 18.2 1.0722 11.7 23 198.25 73.50 42.1 99.6 88.6 104.1 63.1 41.7 25.0 35.6 30.0 19.2 1.0830 7.1 26 186.25 74.50 38.5 101.5 83.6 98.2 59.7 39.7 25.2 32.8 29.4 18.5 1.0812 7.8 27 216.00 76.00 39.4 103.6 90.9 107.7 66.2 39.2 25.9 37.2 30.2 19.0 1.0513 20.8 32 180.50 69.50 38.4 102.0 91.6 103.9 63.4 38.3 21.5 32.5 28.6 17.7 1.0505 21.2 30 205.25 71.25 39.4 104.1 101.8 108.6 66.0 41.5 23.7 36.9 31.6 18.8 1.0484 22.1 35 187.75 69.50 40.5 101.3 96.4 100.1 69.0 39.0 23.1 36.1 30.5 18.2 1.0512 20.9 35 162.75 66.00 36.4 99.1 92.8 99.2 63.1 38.7 21.7 31.1 26.4 16.9 1.0333 29.0 34 195.75 71.00 38.9 101.9 96.4 105.2 64.8 40.8 23.1 36.2 30.8 17.3 1.0468 22.9 32 209.25 71.00 42.1 107.6 97.5 107.0 66.9 40.0 24.4 38.2 31.6 19.3 1.0622 16.0 28 183.75 67.75 38.0 106.8 89.6 102.4 64.2 38.7 22.9 37.2 30.5 18.5 1.0610 16.5 33 211.75 73.50 40.0 106.2 100.5 109.0 65.8 40.6 24.0 37.1 30.1 18.2 1.0551 19.1 28 179.00 68.00 39.1 103.3 95.9 104.9 63.5 38.0 22.1 32.5 30.3 18.4 1.0640 15.2 28 200.50 69.75 41.3 111.4 98.8 104.8 63.4 40.6 24.6 33.0 32.8 19.9 1.0631 15.6 31 140.25 68.25 33.9 86.0 76.4 94.6 57.4 35.3 22.2 27.9 25.9 16.7 1.0584 17.7 32 148.75 70.00 35.5 86.7 80.0 93.4 54.9 36.2 22.1 29.8 26.7 17.1 1.0668 14.0 28 151.25 67.75 34.5 90.2 76.3 95.8 58.4 35.5 22.9 31.1 28.0 17.6 1.0911 3.7 27 159.25 71.50 35.7 89.6 79.7 96.5 55.0 36.7 22.5 29.9 28.2 17.7 1.0811 7.9 34 131.50 67.50 36.2 88.6 74.6 85.3 51.7 34.7 21.4 28.7 27.0 16.5 1.0468 22.9 31 148.00 67.50 38.8 97.4 88.7 94.7 57.5 36.0 21.0 29.2 26.6 17.0 1.0910 3.7 27 133.25 64.75 36.4 93.5 73.9 88.5 50.1 34.5 21.3 30.5 27.9 17.2 1.0790 8.8 29 160.75 69.00 36.7 97.4 83.5 98.7 58.9 35.3 22.6 30.1 26.7 17.6 1.0716 11.9 32 182.00 73.75 38.7 100.5 88.7 99.8 57.5 38.7 33.9 32.5 27.7 18.4 1.0862 5.7 29 160.25 71.25 37.3 93.5 84.5 100.6 58.5 38.8 21.5 30.1 26.4 17.9 1.0719 11.8 27 168.00 71.25 38.1 93.0 79.1 94.5 57.3 36.2 24.5 29.0 30.0 18.8 1.0502 21.3 41 218.50 71.00 39.8 111.7 100.5 108.3 67.1 44.2 25.2 37.5 31.5 18.7 1.0263 32.3 41 247.25 73.50 42.1 117.0 115.6 116.1 71.2 43.3 26.3 37.3 31.7 19.7 1.0101 40.1 49 191.75 65.00 38.4 118.5 113.1 113.8 61.9 38.3 21.9 32.0 29.8 17.0 1.0438 24.2 40 202.25 70.00 38.5 106.5 100.9 106.2 63.5 39.9 22.6 35.1 30.6 19.0 1.0346 28.4 50 196.75 68.25 42.1 105.6 98.8 104.8 66.0 41.5 24.7 33.2 30.5 19.4 1.0202 35.2 46 363.15 72.25 51.2 136.2 148.1 147.7 87.3 49.1 29.6 45.0 29.0 21.4 1.0258 32.6 50 203.00 67.00 40.2 114.8 108.1 102.5 61.3 41.1 24.7 34.1 31.0 18.3 1.0217 34.5 45 262.75 68.75 43.2 128.3 126.2 125.6 72.5 39.6 26.6 36.4 32.7 21.4 1.0250 32.9 44 205.00 29.50 36.6 106.0 104.3 115.5 70.6 42.5 23.7 33.6 28.7 17.4 1.0279 31.6 48 217.00 70.00 37.3 113.3 111.2 114.1 67.7 40.9 25.0 36.7 29.8 18.4 1.0269 32.0 41 212.00 71.50 41.5 106.6 104.3 106.0 65.0 40.2 23.0 35.8 31.5 18.8 1.0814 7.7 39 125.25 68.00 31.5 85.1 76.0 88.2 50.0 34.7 21.0 26.1 23.1 16.1 1.0670 13.9 43 164.25 73.25 35.7 96.6 81.5 97.2 58.4 38.2 23.4 29.7 27.4 18.3 1.0742 10.8 40 133.50 67.50 33.6 88.2 73.7 88.5 53.3 34.5 22.5 27.9 26.2 17.3 1.0665 5.6 39 148.50 71.25 34.6 89.8 79.5 92.7 52.7 37.5 21.9 28.8 26.8 17.9 1.0678 13.6 45 135.75 68.50 32.8 92.3 83.4 90.4 52.0 35.8 20.6 28.8 25.5 16.3 1.0903 4.0 47 127.50 66.75 34.0 83.4 70.4 87.2 50.6 34.4 21.9 26.8 25.8 16.8 1.0756 10.2 47 158.25 72.25 34.9 90.2 86.7 98.3 52.6 37.2 22.4 26.0 25.8 17.3 1.0840 6.6 40 139.25 69.00 34.3 89.2 77.9 91.0 51.4 34.9 21.0 26.7 26.1 17.2 1.0807 8.0 51 137.25 67.75 36.5 89.7 82.0 89.1 49.3 33.7 21.4 29.6 26.0 16.9 1.0848 6.3 49 152.75 73.50 35.1 93.3 79.6 91.6 52.6 37.6 22.6 38.5 27.4 18.5 1.0906 3.9 42 136.25 67.50 37.8 87.6 77.6 88.6 51.9 34.9 22.5 27.7 27.5 18.5 1.0473 22.6 54 198.00 72.00 39.9 107.6 100.0 99.6 57.2 38.0 22.0 35.9 30.2 18.9 1.0524 20.4 58 181.50 68.00 39.1 100.0 99.8 102.5 62.1 39.6 22.5 33.1 28.3 18.5 1.0356 28.0 62 201.25 69.50 40.5 111.5 104.2 105.8 61.8 39.8 22.7 37.7 30.9 19.2 1.0280 31.5 54 202.50 70.75 40.5 115.4 105.3 97.0 59.1 38.0 22.5 31.6 28.8 18.2 1.0430 24.6 61 179.75 65.75 38.4 104.8 98.3 99.6 60.6 37.7 22.9 34.5 29.6 18.5 1.0396 26.1 62 216.00 73.25 41.4 112.3 104.8 103.1 61.6 40.9 23.1 36.2 31.8 20.2 1.0317 29.8 56 178.75 68.50 35.6 102.9 94.7 100.8 60.9 38.0 22.1 32.5 29.8 18.3 1.0298 30.7 54 193.25 70.25 38.0 107.6 102.4 99.4 61.0 39.4 23.6 32.7 29.9 19.1 1.0403 25.8 61 178.00 67.00 37.4 105.3 99.7 99.7 60.8 40.1 22.7 33.6 29.0 18.8 1.0264 32.3 57 205.50 70.00 40.1 105.3 105.5 108.3 65.0 41.2 24.7 35.3 31.1 18.4 1.0313 30.0 55 183.50 67.50 40.9 103.0 100.3 104.2 64.8 40.2 22.7 34.8 30.1 18.7 1.0499 21.5 54 151.50 70.75 35.6 90.0 83.9 93.9 55.0 36.1 21.7 29.6 27.4 17.4 1.0673 13.8 55 154.75 71.50 36.9 95.4 86.6 91.8 54.3 35.4 21.5 32.8 27.4 18.7 1.0847 6.3 54 155.25 69.25 37.5 89.3 78.4 96.1 56.0 37.4 22.4 32.6 28.1 18.1 1.0693 12.9 55 156.75 71.50 36.3 94.4 84.6 94.3 51.2 37.4 21.6 27.3 27.1 17.3 1.0439 24.3 62 167.50 71.50 35.5 97.6 91.5 98.5 56.6 38.6 22.4 31.5 27.3 18.6 1.0788 8.8 55 146.75 68.75 38.7 88.5 82.8 95.5 58.9 37.6 21.6 30.3 27.3 18.3 1.0796 8.5 56 160.75 73.75 36.4 93.6 82.9 96.3 52.9 37.5 23.1 29.7 27.3 18.2 1.0680 13.5 55 125.00 64.00 33.2 87.7 76.0 88.6 50.9 35.4 19.1 29.3 25.7 16.9 1.0720 11.8 61 143.00 65.75 36.5 93.4 83.3 93.0 55.5 35.2 20.9 29.4 27.0 16.8 1.0666 18.5 61 148.25 67.50 36.0 91.6 81.8 94.8 54.5 37.0 21.4 29.3 27.0 18.3 1.0790 8.8 57 162.50 69.50 38.7 91.6 78.8 94.3 56.7 39.7 24.2 30.2 29.2 18.1 1.0483 22.2 69 177.75 68.50 38.7 102.0 95.0 98.3 55.0 38.3 21.8 30.8 25.7 18.8 1.0498 21.5 81 161.25 70.25 37.8 96.4 95.4 99.3 53.5 37.5 21.5 31.4 26.8 18.3 1.0560 18.8 66 171.25 69.25 37.4 102.7 98.6 100.2 56.5 39.3 22.7 30.3 28.7 19.0 1.0283 31.4 67 163.75 67.75 38.4 97.7 95.8 97.1 54.8 38.2 23.7 29.4 27.2 19.0 1.0382 26.8 64 150.25 67.25 38.1 97.1 89.0 96.9 54.8 38.0 22.0 29.9 25.2 17.7 1.0568 18.4 64 190.25 72.75 39.3 103.1 97.8 99.6 58.9 39.0 23.0 34.3 29.6 19.0 1.0377 27.0 70 170.75 70.00 38.7 101.8 94.9 95.0 56.0 36.5 24.1 31.2 27.3 19.2 1.0378 27.0 72 168.00 69.25 38.5 101.4 99.8 96.2 56.3 36.6 22.0 29.7 26.3 18.0 1.0386 26.6 67 167.00 67.50 36.5 98.9 89.7 96.2 54.7 37.8 33.7 32.4 27.7 18.2 1.0648 14.9 72 157.75 67.25 37.7 97.5 88.1 96.9 57.2 37.7 21.8 32.6 28.0 18.8 1.0462 23.1 64 160.00 65.75 36.5 104.3 90.9 93.8 57.8 39.5 23.3 29.2 28.4 18.1 1.0800 8.3 46 176.75 72.50 38.0 97.3 86.0 99.3 61.0 38.4 23.8 30.2 29.3 18.8 1.0666 14.1 48 176.00 73.00 36.7 96.7 86.5 98.3 60.4 39.9 24.4 28.8 29.6 18.7 1.0520 20.5 46 177.00 70.00 37.2 99.7 95.6 102.2 58.3 38.2 22.5 29.1 27.7 17.7 1.0573 18.2 44 179.75 69.50 39.2 101.9 93.2 100.6 58.9 39.7 23.1 31.4 28.4 18.8 1.0795 8.5 47 165.25 70.50 37.5 97.2 83.1 95.4 56.9 38.3 22.1 30.1 28.2 18.4 1.0424 24.9 46 192.50 71.75 38.0 106.6 97.5 100.6 58.9 40.5 24.5 33.3 29.6 19.1 1.0785 9.0 47 184.25 74.50 37.3 99.6 88.8 101.4 57.4 39.6 24.6 30.3 27.9 17.8 1.0991 17.4 53 224.50 77.75 41.1 113.2 99.2 107.5 61.7 42.3 23.2 32.9 30.8 20.4 1.0770 9.6 38 188.75 73.25 37.5 99.1 91.6 102.4 60.6 39.4 22.9 31.6 30.1 18.5 1.0730 11.3 50 162.50 66.50 38.7 99.4 86.7 96.2 62.1 39.3 23.3 30.6 27.8 18.2 1.0582 17.8 46 156.50 68.25 35.9 95.1 88.2 92.8 54.7 37.3 21.9 31.6 27.5 18.2 1.0484 22.2 47 197.00 72.00 40.0 107.5 94.0 103.7 62.7 39.0 22.3 35.3 30.9 18.3 1.0506 21.2 49 198.50 73.50 40.1 106.5 95.0 101.7 59.0 39.4 22.3 32.2 31.0 18.6 1.0524 20.4 48 173.75 72.00 37.0 99.1 92.0 98.3 59.3 38.4 22.4 27.9 26.2 17.0 1.0530 20.1 41 172.75 71.25 36.3 96.7 89.2 98.3 60.0 38.4 23.2 31.0 29.2 18.4 1.0480 22.3 49 196.75 73.75 40.7 103.5 95.5 101.6 59.1 39.8 25.4 31.0 30.3 19.7 1.0412 25.4 43 177.00 69.25 39.6 104.0 98.6 99.5 59.5 36.1 22.0 30.1 27.2 17.7 1.0578 18.0 43 165.50 68.50 31.1 93.1 87.3 96.6 54.7 39.0 24.8 31.0 29.4 18.8 1.0547 19.3 43 200.25 73.50 38.6 105.2 102.8 103.6 61.2 39.3 23.5 30.5 28.5 18.1 1.0569 18.3 52 203.25 74.25 42.0 110.0 101.6 100.7 55.8 38.7 23.4 35.1 29.6 19.1 1.0593 17.3 43 194.00 75.50 38.5 110.1 88.7 102.1 57.5 40.0 24.8 35.1 30.7 19.2 1.0500 21.4 40 168.50 69.25 34.2 97.8 92.3 100.6 57.5 36.8 22.8 32.1 26.0 17.3 1.0538 19.7 43 170.75 68.50 37.2 96.3 90.6 99.3 61.9 38.0 22.3 33.3 28.2 18.1 1.0355 28.0 43 183.25 70.00 37.1 108.0 105.0 103.0 63.7 40.0 23.6 33.5 27.8 17.4 1.0486 22.1 47 178.25 70.00 40.2 99.7 95.0 98.6 62.3 38.1 23.9 35.3 31.1 19.8 1.0503 21.3 42 163.00 70.25 35.3 93.5 89.6 99.8 61.5 37.8 21.9 30.7 27.6 17.4 1.0384 26.7 48 175.25 71.75 38.0 100.7 92.4 97.5 59.3 38.1 21.8 31.8 27.3 17.5 1.0607 16.7 40 158.00 69.25 36.3 97.0 86.6 92.6 55.9 36.3 22.1 29.8 26.3 17.3 1.0529 20.1 48 177.25 72.75 36.8 96.0 90.0 99.7 58.8 38.4 22.8 29.9 28.0 18.1 1.0671 13.9 51 179.00 72.00 41.0 99.2 90.0 96.4 56.8 38.8 23.3 33.4 29.8 19.5 1.0404 25.8 40 191.00 74.00 38.3 95.4 92.4 104.3 64.6 41.1 24.8 33.6 29.5 18.5 1.0575 18.1 44 187.50 72.25 38.0 101.8 87.5 101.0 58.5 39.2 24.5 32.1 28.6 18.0 1.0358 27.9 52 206.50 74.50 40.8 104.3 99.2 104.1 58.5 39.3 24.6 33.9 31.2 19.5 1.0414 25.3 44 185.25 71.50 39.5 99.2 98.1 101.4 57.1 40.5 23.2 33.0 29.6 18.4 1.0652 14.7 40 160.25 68.75 36.9 99.3 83.3 97.5 60.5 38.7 22.6 34.4 28.0 17.6 1.0623 16.0 47 151.50 66.75 36.9 94.0 86.1 95.2 58.1 36.5 22.1 30.6 27.5 17.6 1.0674 13.8 50 161.00 66.50 37.7 98.9 84.1 94.0 58.5 36.6 23.5 34.4 29.2 18.0 1.0587 17.5 46 167.00 67.00 36.6 101.0 89.9 100.0 60.7 36.0 21.9 35.6 30.2 17.6 1.0373 27.2 42 177.50 68.75 38.9 98.7 92.1 98.5 60.7 36.8 22.2 33.8 30.3 17.2 1.0590 17.4 43 152.25 67.75 37.5 95.9 78.0 93.2 53.5 35.8 20.8 33.9 28.2 17.4 1.0515 20.8 40 192.25 73.25 39.8 103.9 93.5 99.5 61.7 39.0 21.8 33.3 29.6 18.1 1.0648 14.9 42 165.25 69.75 38.3 96.2 87.0 97.8 57.4 36.9 22.2 31.6 27.8 17.7 1.0575 18.1 49 171.75 71.50 35.5 97.8 90.1 95.8 57.0 38.7 23.2 27.5 26.5 17.6 1.0472 22.7 40 171.25 70.50 36.3 94.6 90.3 99.1 60.3 38.5 23.0 31.2 28.4 17.1 1.0452 23.6 47 197.00 73.25 37.8 103.6 99.8 103.2 61.2 38.1 22.6 33.5 28.6 17.9 1.0398 26.1 50 157.00 66.75 37.8 100.4 89.4 92.3 56.1 35.6 20.5 33.6 29.3 17.3 1.0435 24.4 41 168.25 69.50 36.5 98.4 87.2 98.4 56.0 36.9 23.0 34.0 29.8 18.1 1.0374 27.1 44 186.00 69.75 37.8 104.6 101.1 102.1 58.9 37.9 22.7 30.9 28.8 17.6 1.0491 21.8 39 166.75 70.75 37.0 92.9 86.1 95.6 58.8 36.1 22.4 32.7 28.3 17.1 1.0325 29.4 43 187.75 74.00 37.7 97.8 98.6 100.6 63.6 39.2 23.8 34.3 28.4 17.7 1.0481 22.4 40 168.25 71.25 34.3 98.3 88.5 98.3 58.1 38.4 22.5 31.7 27.4 17.6 1.0522 20.4 49 212.75 75.00 40.8 104.7 106.6 107.7 66.5 42.5 24.5 35.5 29.8 18.7 1.0422 24.9 40 176.75 71.00 37.4 98.6 93.1 101.6 59.1 39.6 21.6 30.8 27.9 16.6 1.0571 18.3 40 173.25 69.50 36.5 99.5 93.0 99.3 60.4 38.2 22.0 32.0 28.5 17.8 1.0459 23.3 52 167.00 67.75 37.5 102.7 91.0 98.9 57.1 36.7 22.3 31.6 27.5 17.9 1.0775 9.4 23 159.75 72.25 35.5 92.1 77.1 93.9 56.1 36.1 22.7 30.5 27.2 18.2 1.0754 10.3 23 188.15 77.50 38.0 96.6 85.3 102.5 59.1 37.6 23.2 31.8 29.7 18.3 1.0664 14.2 24 156.00 70.75 35.7 92.7 81.9 95.3 56.4 36.5 22.0 33.5 28.3 17.3 1.0550 19.2 24 208.50 72.75 39.2 102.0 99.1 110.1 71.2 43.5 25.2 36.1 30.3 18.7 1.0322 29.6 25 206.50 69.75 40.9 110.9 100.5 106.2 68.4 40.8 24.6 33.3 29.7 18.4 1.0873 5.3 25 143.75 72.50 35.2 92.3 76.5 92.1 51.9 35.7 22.0 25.8 25.2 16.9 1.0416 25.2 26 223.00 70.25 40.6 114.1 106.8 113.9 67.6 42.7 24.7 36.0 30.4 18.4 1.0776 9.4 26 152.25 69.00 35.4 92.9 77.6 93.5 56.9 35.9 20.4 31.6 29.0 17.8 1.0542 19.6 26 241.75 74.50 41.8 108.3 102.9 114.4 72.9 43.5 25.1 38.5 33.8 19.6 1.0758 10.1 27 146.00 72.25 34.1 88.5 72.8 91.1 53.6 36.8 23.8 27.8 26.3 17.4 1.0610 16.5 27 156.75 67.25 37.9 94.0 88.2 95.2 56.8 37.4 22.8 30.6 28.3 17.9 1.0510 21.0 27 200.25 73.50 38.2 101.1 100.1 105.0 62.1 40.0 24.9 33.7 29.2 19.4 1.0594 17.3 28 171.50 75.25 35.6 92.1 83.5 98.3 57.3 37.8 21.7 32.2 27.7 17.7 1.0287 31.2 28 205.75 69.00 38.5 105.6 105.0 106.4 68.6 40.0 25.2 35.2 30.7 19.1 1.0761 10.0 28 182.50 72.25 37.0 98.5 90.8 102.5 60.8 38.5 25.0 31.6 28.0 18.6 1.0704 12.5 30 136.50 68.75 35.9 88.7 76.6 89.8 50.1 34.8 21.8 27.0 34.9 16.9 1.0477 22.5 31 177.25 71.50 36.2 101.1 92.4 99.3 59.4 39.0 24.6 30.1 28.2 18.2 1.0775 9.4 31 151.25 72.25 35.0 94.0 81.2 91.5 52.5 36.6 21.0 27.0 26.3 16.5 1.0653 14.6 33 196.00 73.00 38.5 103.8 95.6 105.1 61.4 40.6 25.0 31.3 29.2 19.1 1.0690 13.0 33 184.25 68.75 40.7 98.9 92.1 103.5 64.0 37.3 23.5 33.5 30.6 19.7 1.0644 15.1 34 140.00 70.50 36.0 89.2 83.4 89.6 52.4 35.6 20.4 28.3 26.2 16.5 1.0370 27.3 34 218.75 72.00 39.5 111.4 106.0 108.8 63.8 42.0 23.4 34.0 31.2 18.5 1.0549 19.2 35 217.00 73.75 40.5 107.5 95.1 104.5 64.8 41.3 25.6 36.4 33.7 19.4 1.0492 21.8 35 166.25 68.00 38.5 99.1 90.4 95.6 55.5 34.2 21.9 30.2 28.7 17.7 1.0525 20.3 35 224.75 72.25 43.9 108.2 100.4 106.8 63.3 41.7 24.6 37.2 33.1 19.8 1.0180 34.3 35 228.25 69.50 40.4 114.9 115.9 111.9 74.4 40.6 24.0 36.1 31.8 18.8 1.0610 16.5 35 172.75 69.50 37.6 99.1 90.8 98.1 60.1 39.1 23.4 32.5 29.8 17.4 1.0926 3.0 35 152.25 67.75 37.0 92.2 81.9 92.8 54.7 36.2 22.1 30.4 27.4 17.7 1.0983 .7 35 125.75 65.50 34.0 90.8 75.0 89.2 50.0 34.8 22.0 24.8 25.9 16.9 1.0521 20.5 35 177.25 71.00 38.4 100.5 90.3 98.7 57.8 37.3 22.4 31.0 28.7 17.7 1.0603 16.9 36 176.25 71.50 38.7 98.2 90.3 99.9 59.2 37.7 21.5 32.4 28.4 17.8 1.0414 25.3 36 226.75 71.75 41.5 115.3 108.8 114.4 69.2 42.4 24.0 35.4 21.0 20.1 1.0763 9.9 37 145.25 69.25 36.0 96.8 79.4 89.2 50.3 34.8 22.2 31.0 26.9 16.9 1.0689 13.1 37 151.00 67.00 35.3 92.6 83.2 96.4 60.0 38.1 22.0 31.5 26.6 16.7 1.0316 29.9 37 241.25 71.50 42.1 119.2 110.3 113.9 69.8 42.6 24.8 34.4 29.5 18.4 1.0477 22.5 38 187.25 69.25 38.0 102.7 92.7 101.9 64.7 39.5 24.7 34.8 30.3 18.1 1.0603 16.9 39 234.75 74.50 42.8 109.5 104.5 109.9 69.5 43.1 25.8 39.1 32.5 19.9 1.0387 26.6 39 219.25 74.25 40.0 108.5 104.6 109.8 68.1 42.8 24.1 35.6 29.0 19.0 1.1089 .0 40 118.50 68.00 33.8 79.3 69.4 85.0 47.2 33.5 20.2 27.7 24.6 16.5 1.0725 11.5 40 145.75 67.25 35.5 95.5 83.6 91.6 54.1 36.2 21.8 31.4 28.3 17.2 1.0713 12.1 40 159.25 69.75 35.3 92.3 86.8 96.1 58.0 39.4 22.7 30.0 26.4 17.4 1.0587 17.5 40 170.50 74.25 37.7 98.9 90.4 95.5 55.4 38.9 22.4 30.5 28.9 17.7 1.0794 8.6 40 167.50 71.50 39.4 89.5 83.7 98.1 57.3 39.7 22.6 32.9 29.3 18.2 1.0453 23.6 41 232.75 74.25 41.9 117.5 109.3 108.8 67.7 41.3 24.7 37.2 31.8 20.0 1.0524 20.4 41 210.50 72.00 38.5 107.4 98.9 104.1 63.5 39.8 23.5 36.4 30.4 19.1 1.0520 20.5 41 202.25 72.50 40.8 109.2 98.0 101.8 62.8 41.3 24.8 36.6 32.4 18.8 1.0434 24.4 41 185.00 68.25 38.0 103.4 101.2 103.1 61.5 40.4 22.9 33.4 29.2 18.5 1.0728 11.4 41 153.00 69.25 36.4 91.4 80.6 92.3 54.3 36.3 21.8 29.6 27.3 17.9 1.0140 38.1 42 244.25 76.00 41.8 115.2 113.7 112.4 68.5 45.0 25.5 37.1 31.2 19.9 1.0624 15.9 42 193.50 70.50 40.7 104.9 94.1 102.7 60.6 38.6 24.7 34.0 30.1 18.7 1.0429 24.7 42 224.75 74.75 38.5 106.7 105.7 111.8 65.3 43.3 26.0 33.7 29.9 18.5 1.0470 22.8 42 162.75 72.75 35.4 92.2 85.6 96.5 60.2 38.9 22.4 31.7 27.1 17.1 1.0411 25.5 42 180.00 68.25 38.5 101.6 96.6 100.6 61.1 38.4 24.1 32.9 29.8 18.8 1.0488 22.0 42 156.25 69.00 35.5 97.8 86.0 96.2 57.7 38.6 24.0 31.2 27.3 17.4 1.0583 17.7 42 168.00 71.50 36.5 92.0 89.7 101.0 62.3 38.0 22.3 30.8 27.8 16.9 1.0841 6.6 42 167.25 72.75 37.6 94.0 78.0 99.0 57.5 40.0 22.5 30.6 30.0 18.5 1.0462 23.6 43 170.75 67.50 37.4 103.7 89.7 94.2 58.5 39.0 24.1 33.8 28.8 18.8 1.0709 12.2 43 178.25 70.25 37.8 102.7 89.2 99.2 60.2 39.2 23.8 31.7 28.4 18.6 1.0484 22.1 43 150.00 69.25 35.2 91.1 85.7 96.9 55.5 35.7 22.0 29.4 26.6 17.4 1.0340 28.7 43 200.50 71.50 37.9 107.2 103.1 105.5 68.8 38.3 23.7 32.1 28.9 18.7 1.0854 6.0 44 184.00 74.00 37.9 100.8 89.1 102.6 60.6 39.0 24.0 32.9 29.2 18.4 1.0209 34.8 44 223.00 69.75 40.9 121.6 113.9 107.1 63.5 40.3 21.8 34.8 30.7 17.4 1.0610 16.6 44 208.75 73.00 41.9 105.6 96.3 102.0 63.3 39.8 24.1 37.3 23.1 19.4 1.0250 32.9 44 166.00 65.50 39.1 100.6 93.9 100.1 58.9 37.6 21.4 33.1 29.5 17.3 1.0254 32.8 47 195.00 72.50 40.2 102.7 101.3 101.7 60.7 39.4 23.3 36.7 31.6 18.4 1.0771 9.6 47 160.50 70.25 36.0 99.8 83.9 91.8 53.0 36.2 22.5 31.4 27.5 17.7 1.0742 10.8 47 159.75 70.75 34.5 92.9 84.4 94.0 56.0 38.2 22.6 29.0 26.2 17.6 1.0829 7.1 49 140.50 68.00 35.8 91.2 79.4 89.0 51.1 35.0 21.7 30.9 28.8 17.4 1.0373 27.2 49 216.25 74.50 40.2 115.6 104.0 109.0 63.7 40.3 23.2 36.8 31.0 18.9 1.0543 19.5 49 168.25 71.75 38.3 98.3 89.7 99.1 56.3 38.8 23.0 29.5 27.9 18.6 1.0561 18.7 50 194.75 70.75 39.0 103.7 97.6 104.2 60.0 40.9 25.5 32.7 30.0 19.0 1.0543 19.5 50 172.75 73.00 37.4 98.7 87.6 96.1 57.1 38.1 21.8 28.6 26.7 18.0 .9950 47.5 51 219.00 64.00 41.2 119.8 122.1 112.8 62.5 36.9 23.6 34.7 29.1 18.4 1.0678 13.6 51 149.25 69.75 34.8 92.8 81.1 96.3 53.8 36.5 21.5 31.3 26.3 17.8 1.0819 7.5 51 154.50 70.00 36.9 93.3 81.5 94.4 54.7 39.0 22.6 27.5 25.9 18.6 1.0433 24.5 52 199.25 71.75 39.4 106.8 100.0 105.0 63.9 39.2 22.9 35.7 30.4 19.2 1.0646 15.0 53 154.50 69.25 37.6 93.9 88.7 94.5 53.7 36.2 22.0 28.5 25.7 17.1 1.0706 12.4 54 153.25 70.50 38.5 99.0 91.8 96.2 57.7 38.1 23.9 31.4 29.9 18.9 1.0399 26.0 54 230.00 72.25 42.5 119.9 110.4 105.5 64.2 42.7 27.0 38.4 32.0 19.6 1.0726 11.5 54 161.75 67.50 37.4 94.2 87.6 95.6 59.7 40.2 23.4 27.9 27.0 17.8 1.0874 5.2 55 142.25 67.25 35.2 92.7 82.8 91.9 54.4 35.2 22.5 29.4 26.8 17.0 1.0740 10.9 55 179.75 68.75 41.1 106.9 95.3 98.2 57.4 37.1 21.8 34.1 31.1 19.2 1.0703 12.5 55 126.50 66.75 33.4 88.8 78.2 87.5 50.8 33.0 19.7 25.3 22.0 15.8 1.0650 14.8 55 169.50 68.25 37.2 101.7 91.1 97.1 56.6 38.5 22.6 33.4 29.3 18.8 1.0418 25.2 55 198.50 74.25 38.3 105.3 96.7 106.6 64.0 42.6 23.4 33.2 30.0 18.4 1.0647 14.9 56 174.50 69.50 38.1 104.0 89.4 98.4 58.4 37.4 22.5 34.6 30.1 18.8 1.0601 17.0 56 167.75 68.50 37.4 98.6 93.0 97.0 55.4 38.8 23.2 32.4 29.7 19.0 1.0745 10.6 57 147.75 65.75 35.2 99.6 86.4 90.1 53.0 35.0 21.3 31.7 27.3 16.9 1.0620 16.1 57 182.25 71.75 39.4 103.4 96.7 100.7 59.3 38.6 22.8 31.8 29.1 19.0 1.0636 15.4 58 175.50 71.50 38.0 100.2 88.1 97.8 57.1 38.9 23.6 30.9 29.6 18.0 1.0384 26.7 58 161.75 67.25 35.1 94.9 94.9 100.2 56.8 35.9 21.0 27.8 26.1 17.6 1.0403 25.8 60 157.75 67.50 40.4 97.2 93.3 94.0 54.3 35.7 21.0 31.3 28.7 18.3 1.0563 18.6 62 168.75 67.50 38.3 104.7 95.6 93.7 54.4 37.1 22.7 30.3 26.3 18.3 1.0424 24.8 62 191.50 72.25 40.6 104.0 98.2 101.1 59.3 40.3 23.0 32.6 28.5 19.0 1.0372 27.3 63 219.15 69.50 40.2 117.6 113.8 111.8 63.4 41.1 22.3 35.1 29.6 18.5 1.0705 12.4 64 155.25 69.50 37.9 95.8 82.8 94.5 61.2 39.1 22.3 29.8 28.9 18.3 1.0316 29.9 65 189.75 65.75 40.8 106.4 100.5 100.5 59.2 38.1 24.0 35.9 30.5 19.1 1.0599 17.0 65 127.50 65.75 34.7 93.0 79.7 87.6 50.7 33.4 20.1 28.5 24.8 16.5 1.0207 35.0 65 224.50 68.25 38.8 119.6 118.0 114.3 61.3 42.1 23.4 34.9 30.1 19.4 1.0304 30.4 66 234.25 72.00 41.4 119.7 109.0 109.1 63.7 42.4 24.6 35.6 30.7 19.5 1.0256 32.6 67 227.75 72.75 41.3 115.8 113.4 109.8 65.6 46.0 25.4 35.3 29.8 19.5 1.0334 29.0 67 199.50 68.50 40.7 118.3 106.1 101.6 58.2 38.8 24.1 32.1 29.3 18.5 1.0641 15.2 68 155.50 69.25 36.3 97.4 84.3 94.4 54.3 37.5 22.6 29.2 27.3 18.5 1.0308 30.2 69 215.50 70.50 40.8 113.7 107.6 110.0 63.3 44.0 22.6 37.5 32.6 18.8 1.0736 11.0 70 134.25 67.00 34.9 89.2 83.6 88.8 49.6 34.8 21.5 25.6 25.7 18.5 1.0236 33.6 72 201.00 69.75 40.9 108.5 105.0 104.5 59.6 40.8 23.2 35.2 28.6 20.1 1.0328 29.3 72 186.75 66.00 38.9 111.1 111.5 101.7 60.3 37.3 21.5 31.3 27.2 18.0 1.0399 26.0 72 190.75 70.50 38.9 108.3 101.3 97.8 56.0 41.6 22.7 30.5 29.4 19.8 1.0271 31.9 74 207.50 70.00 40.8 112.4 108.5 107.1 59.3 42.2 24.6 33.7 30.0 20.9 Roger W. Johnson Department of Mathematics & Computer Science South Dakota School of Mines & Technology 501 East St. Joseph Street Rapid City, SD 57701 email address: rwjohnso@silver.sdsmt.edu web address: http://silver.sdsmt.edu/~rwjohnso