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.

Density	PCTBF	Age	Weight	Height	Neck	Chest	Abdomen	Hip	Thigh	Knee	Ankle	Biceps	Forearm	Wrist
1.0708	12.3	23	154.25	67.75	36.2	93.1	85.2	94.5	59	37.3	21.9	32	27.4	17.1
1.0853	6.1	22	173.25	72.25	38.5	93.6	83	98.7	58.7	37.3	23.4	30.5	28.9	18.2
1.0414	25.3	22	154	66.25	34	95.8	87.9	99.2	59.6	38.9	24	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
1.034	28.7	24	184.25	71.25	34.4	97.3	100	101.9	63.2	42.2	24	32.2	27.7	17.7
1.0502	20.9	24	210.25	74.75	39	104.5	94.4	107.8	66	42	25.6	35.7	30.6	18.8
1.0549	19.2	26	181	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	72.5	37.8	99.6	88.5	97.1	60	39.4	23.2	30.5	29	18.8
1.09	4.1	25	191	74	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	73.5	42.1	99.6	88.6	104.1	63.1	41.7	25	35.6	30	19.2
1.083	7.1	26	186.25	74.5	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	76	39.4	103.6	90.9	107.7	66.2	39.2	25.9	37.2	30.2	19
1.0513	20.8	32	180.5	69.5	38.4	102	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	41.5	23.7	36.9	31.6	18.8
1.0484	22.1	35	187.75	69.5	40.5	101.3	96.4	100.1	69	39	23.1	36.1	30.5	18.2
1.0512	20.9	35	162.75	66	36.4	99.1	92.8	99.2	63.1	38.7	21.7	31.1	26.4	16.9
1.0333	29	34	195.75	71	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	42.1	107.6	97.5	107	66.9	40	24.4	38.2	31.6	19.3
1.0622	16	28	183.75	67.75	38	106.8	89.6	102.4	64.2	38.7	22.9	37.2	30.5	18.5
1.061	16.5	33	211.75	73.5	40	106.2	100.5	109	65.8	40.6	24	37.1	30.1	18.2
1.0551	19.1	28	179	68	39.1	103.3	95.9	104.9	63.5	38	22.1	32.5	30.3	18.4
1.064	15.2	28	200.5	69.75	41.3	111.4	98.8	104.8	63.4	40.6	24.6	33	32.8	19.9
1.0631	15.6	31	140.25	68.25	33.9	86	76.4	94.6	57.4	35.3	22.2	27.9	25.9	16.7
1.0584	17.7	32	148.75	70	35.5	86.7	80	93.4	54.9	36.2	22.1	29.8	26.7	17.1
1.0668	14	28	151.25	67.75	34.5	90.2	76.3	95.8	58.4	35.5	22.9	31.1	28	17.6
1.0911	3.7	27	159.25	71.5	35.7	89.6	79.7	96.5	55	36.7	22.5	29.9	28.2	17.7
1.0811	7.9	34	131.5	67.5	36.2	88.6	74.6	85.3	51.7	34.7	21.4	28.7	27	16.5
1.0468	22.9	31	148	67.5	38.8	97.4	88.7	94.7	57.5	36	21	29.2	26.6	17
1.091	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
1.079	8.8	29	160.75	69	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	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	71.25	38.1	93	79.1	94.5	57.3	36.2	24.5	29	30	18.8
1.0502	21.3	41	218.5	71	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	73.5	42.1	117	115.6	116.1	71.2	43.3	26.3	37.3	31.7	19.7
1.0101	40.1	49	191.75	65	38.4	118.5	113.1	113.8	61.9	38.3	21.9	32	29.8	17
1.0438	24.2	40	202.25	70	38.5	106.5	100.9	106.2	63.5	39.9	22.6	35.1	30.6	19
1.0346	28.4	50	196.75	68.25	42.1	105.6	98.8	104.8	66	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	29	21.4
1.0258	32.6	50	203	67	40.2	114.8	108.1	102.5	61.3	41.1	24.7	34.1	31	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
1.025	32.9	44	205	29.5	36.6	106	104.3	115.5	70.6	42.5	23.7	33.6	28.7	17.4
1.0279	31.6	48	217	70	37.3	113.3	111.2	114.1	67.7	40.9	25	36.7	29.8	18.4
1.0269	32	41	212	71.5	41.5	106.6	104.3	106	65	40.2	23	35.8	31.5	18.8
1.0814	7.7	39	125.25	68	31.5	85.1	76	88.2	50	34.7	21	26.1	23.1	16.1
1.067	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	133.5	67.5	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	148.5	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	68.5	32.8	92.3	83.4	90.4	52	35.8	20.6	28.8	25.5	16.3
1.0903	4	47	127.5	66.75	34	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	25.8	17.3
1.084	6.6	40	139.25	69	34.3	89.2	77.9	91	51.4	34.9	21	26.7	26.1	17.2
1.0807	8	51	137.25	67.75	36.5	89.7	82	89.1	49.3	33.7	21.4	29.6	26	16.9
1.0848	6.3	49	152.75	73.5	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	67.5	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	72	39.9	107.6	100	99.6	57.2	38	22	35.9	30.2	18.9
1.0524	20.4	58	181.5	68	39.1	100	99.8	102.5	62.1	39.6	22.5	33.1	28.3	18.5
1.0356	28	62	201.25	69.5	40.5	111.5	104.2	105.8	61.8	39.8	22.7	37.7	30.9	19.2
1.028	31.5	54	202.5	70.75	40.5	115.4	105.3	97	59.1	38	22.5	31.6	28.8	18.2
1.043	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	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	68.5	35.6	102.9	94.7	100.8	60.9	38	22.1	32.5	29.8	18.3
1.0298	30.7	54	193.25	70.25	38	107.6	102.4	99.4	61	39.4	23.6	32.7	29.9	19.1
1.0403	25.8	61	178	67	37.4	105.3	99.7	99.7	60.8	40.1	22.7	33.6	29	18.8
1.0264	32.3	57	205.5	70	40.1	105.3	105.5	108.3	65	41.2	24.7	35.3	31.1	18.4
1.0313	30	55	183.5	67.5	40.9	103	100.3	104.2	64.8	40.2	22.7	34.8	30.1	18.7
1.0499	21.5	54	151.5	70.75	35.6	90	83.9	93.9	55	36.1	21.7	29.6	27.4	17.4
1.0673	13.8	55	154.75	71.5	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	37.4	22.4	32.6	28.1	18.1
1.0693	12.9	55	156.75	71.5	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	167.5	71.5	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
1.068	13.5	55	125	64	33.2	87.7	76	88.6	50.9	35.4	19.1	29.3	25.7	16.9
1.072	11.8	61	143	65.75	36.5	93.4	83.3	93	55.5	35.2	20.9	29.4	27	16.8
1.0666	18.5	61	148.25	67.5	36	91.6	81.8	94.8	54.5	37	21.4	29.3	27	18.3
1.079	8.8	57	162.5	69.5	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	68.5	38.7	102	95	98.3	55	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
1.056	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
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
1.0382	26.8	64	150.25	67.25	38.1	97.1	89	96.9	54.8	38	22	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	23	34.3	29.6	19
1.0377	27	70	170.75	70	38.7	101.8	94.9	95	56	36.5	24.1	31.2	27.3	19.2
1.0378	27	72	168	69.25	38.5	101.4	99.8	96.2	56.3	36.6	22	29.7	26.3	18
1.0386	26.6	67	167	67.5	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	18.8
1.0462	23.1	64	160	65.75	36.5	104.3	90.9	93.8	57.8	39.5	23.3	29.2	28.4	18.1
1.08	8.3	46	176.75	72.5	38	97.3	86	99.3	61	38.4	23.8	30.2	29.3	18.8
1.0666	14.1	48	176	73	36.7	96.7	86.5	98.3	60.4	39.9	24.4	28.8	29.6	18.7
1.052	20.5	46	177	70	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	69.5	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	70.5	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	192.5	71.75	38	106.6	97.5	100.6	58.9	40.5	24.5	33.3	29.6	19.1
1.0785	9	47	184.25	74.5	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	224.5	77.75	41.1	113.2	99.2	107.5	61.7	42.3	23.2	32.9	30.8	20.4
1.077	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
1.073	11.3	50	162.5	66.5	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	156.5	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	72	40	107.5	94	103.7	62.7	39	22.3	35.3	30.9	18.3
1.0506	21.2	49	198.5	73.5	40.1	106.5	95	101.7	59	39.4	22.3	32.2	31	18.6
1.0524	20.4	48	173.75	72	37	99.1	92	98.3	59.3	38.4	22.4	27.9	26.2	17
1.053	20.1	41	172.75	71.25	36.3	96.7	89.2	98.3	60	38.4	23.2	31	29.2	18.4
1.048	22.3	49	196.75	73.75	40.7	103.5	95.5	101.6	59.1	39.8	25.4	31	30.3	19.7
1.0412	25.4	43	177	69.25	39.6	104	98.6	99.5	59.5	36.1	22	30.1	27.2	17.7
1.0578	18	43	165.5	68.5	31.1	93.1	87.3	96.6	54.7	39	24.8	31	29.4	18.8
1.0547	19.3	43	200.25	73.5	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	110	101.6	100.7	55.8	38.7	23.4	35.1	29.6	19.1
1.0593	17.3	43	194	75.5	38.5	110.1	88.7	102.1	57.5	40	24.8	35.1	30.7	19.2
1.05	21.4	40	168.5	69.25	34.2	97.8	92.3	100.6	57.5	36.8	22.8	32.1	26	17.3
1.0538	19.7	43	170.75	68.5	37.2	96.3	90.6	99.3	61.9	38	22.3	33.3	28.2	18.1
1.0355	28	43	183.25	70	37.1	108	105	103	63.7	40	23.6	33.5	27.8	17.4
1.0486	22.1	47	178.25	70	40.2	99.7	95	98.6	62.3	38.1	23.9	35.3	31.1	19.8
1.0503	21.3	42	163	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	100.7	92.4	97.5	59.3	38.1	21.8	31.8	27.3	17.5
1.0607	16.7	40	158	69.25	36.3	97	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	90	99.7	58.8	38.4	22.8	29.9	28	18.1
1.0671	13.9	51	179	72	41	99.2	90	96.4	56.8	38.8	23.3	33.4	29.8	19.5
1.0404	25.8	40	191	74	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	187.5	72.25	38	101.8	87.5	101	58.5	39.2	24.5	32.1	28.6	18
1.0358	27.9	52	206.5	74.5	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	71.5	39.5	99.2	98.1	101.4	57.1	40.5	23.2	33	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	17.6
1.0623	16	47	151.5	66.75	36.9	94	86.1	95.2	58.1	36.5	22.1	30.6	27.5	17.6
1.0674	13.8	50	161	66.5	37.7	98.9	84.1	94	58.5	36.6	23.5	34.4	29.2	18
1.0587	17.5	46	167	67	36.6	101	89.9	100	60.7	36	21.9	35.6	30.2	17.6
1.0373	27.2	42	177.5	68.75	38.9	98.7	92.1	98.5	60.7	36.8	22.2	33.8	30.3	17.2
1.059	17.4	43	152.25	67.75	37.5	95.9	78	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	21.8	33.3	29.6	18.1
1.0648	14.9	42	165.25	69.75	38.3	96.2	87	97.8	57.4	36.9	22.2	31.6	27.8	17.7
1.0575	18.1	49	171.75	71.5	35.5	97.8	90.1	95.8	57	38.7	23.2	27.5	26.5	17.6
1.0472	22.7	40	171.25	70.5	36.3	94.6	90.3	99.1	60.3	38.5	23	31.2	28.4	17.1
1.0452	23.6	47	197	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	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	69.5	36.5	98.4	87.2	98.4	56	36.9	23	34	29.8	18.1
1.0374	27.1	44	186	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	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	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	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	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	69.5	36.5	99.5	93	99.3	60.4	38.2	22	32	28.5	17.8
1.0459	23.3	52	167	67.75	37.5	102.7	91	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	77.5	38	96.6	85.3	102.5	59.1	37.6	23.2	31.8	29.7	18.3
1.0664	14.2	24	156	70.75	35.7	92.7	81.9	95.3	56.4	36.5	22	33.5	28.3	17.3
1.055	19.2	24	208.5	72.75	39.2	102	99.1	110.1	71.2	43.5	25.2	36.1	30.3	18.7
1.0322	29.6	25	206.5	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	72.5	35.2	92.3	76.5	92.1	51.9	35.7	22	25.8	25.2	16.9
1.0416	25.2	26	223	70.25	40.6	114.1	106.8	113.9	67.6	42.7	24.7	36	30.4	18.4
1.0776	9.4	26	152.25	69	35.4	92.9	77.6	93.5	56.9	35.9	20.4	31.6	29	17.8
1.0542	19.6	26	241.75	74.5	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	72.25	34.1	88.5	72.8	91.1	53.6	36.8	23.8	27.8	26.3	17.4
1.061	16.5	27	156.75	67.25	37.9	94	88.2	95.2	56.8	37.4	22.8	30.6	28.3	17.9
1.051	21	27	200.25	73.5	38.2	101.1	100.1	105	62.1	40	24.9	33.7	29.2	19.4
1.0594	17.3	28	171.5	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	38.5	105.6	105	106.4	68.6	40	25.2	35.2	30.7	19.1
1.0761	10	28	182.5	72.25	37	98.5	90.8	102.5	60.8	38.5	25	31.6	28	18.6
1.0704	12.5	30	136.5	68.75	35.9	88.7	76.6	89.8	50.1	34.8	21.8	27	34.9	16.9
1.0477	22.5	31	177.25	71.5	36.2	101.1	92.4	99.3	59.4	39	24.6	30.1	28.2	18.2
1.0775	9.4	31	151.25	72.25	35	94	81.2	91.5	52.5	36.6	21	27	26.3	16.5
1.0653	14.6	33	196	73	38.5	103.8	95.6	105.1	61.4	40.6	25	31.3	29.2	19.1
1.069	13	33	184.25	68.75	40.7	98.9	92.1	103.5	64	37.3	23.5	33.5	30.6	19.7
1.0644	15.1	34	140	70.5	36	89.2	83.4	89.6	52.4	35.6	20.4	28.3	26.2	16.5
1.037	27.3	34	218.75	72	39.5	111.4	106	108.8	63.8	42	23.4	34	31.2	18.5
1.0549	19.2	35	217	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	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
1.018	34.3	35	228.25	69.5	40.4	114.9	115.9	111.9	74.4	40.6	24	36.1	31.8	18.8
1.061	16.5	35	172.75	69.5	37.6	99.1	90.8	98.1	60.1	39.1	23.4	32.5	29.8	17.4
1.0926	3	35	152.25	67.75	37	92.2	81.9	92.8	54.7	36.2	22.1	30.4	27.4	17.7
1.0983	0.7	35	125.75	65.5	34	90.8	75	89.2	50	34.8	22	24.8	25.9	16.9
1.0521	20.5	35	177.25	71	38.4	100.5	90.3	98.7	57.8	37.3	22.4	31	28.7	17.7
1.0603	16.9	36	176.25	71.5	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	35.4	21	20.1
1.0763	9.9	37	145.25	69.25	36	96.8	79.4	89.2	50.3	34.8	22.2	31	26.9	16.9
1.0689	13.1	37	151	67	35.3	92.6	83.2	96.4	60	38.1	22	31.5	26.6	16.7
1.0316	29.9	37	241.25	71.5	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	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	74.5	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	108.5	104.6	109.8	68.1	42.8	24.1	35.6	29	19
1.1089	0	40	118.5	68	33.8	79.3	69.4	85	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	39.4	22.7	30	26.4	17.4
1.0587	17.5	40	170.5	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	167.5	71.5	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
1.0524	20.4	41	210.5	72	38.5	107.4	98.9	104.1	63.5	39.8	23.5	36.4	30.4	19.1
1.052	20.5	41	202.25	72.5	40.8	109.2	98	101.8	62.8	41.3	24.8	36.6	32.4	18.8
1.0434	24.4	41	185	68.25	38	103.4	101.2	103.1	61.5	40.4	22.9	33.4	29.2	18.5
1.0728	11.4	41	153	69.25	36.4	91.4	80.6	92.3	54.3	36.3	21.8	29.6	27.3	17.9
1.014	38.1	42	244.25	76	41.8	115.2	113.7	112.4	68.5	45	25.5	37.1	31.2	19.9
1.0624	15.9	42	193.5	70.5	40.7	104.9	94.1	102.7	60.6	38.6	24.7	34	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	33.7	29.9	18.5
1.047	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	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	42	156.25	69	35.5	97.8	86	96.2	57.7	38.6	24	31.2	27.3	17.4
1.0583	17.7	42	168	71.5	36.5	92	89.7	101	62.3	38	22.3	30.8	27.8	16.9
1.0841	6.6	42	167.25	72.75	37.6	94	78	99	57.5	40	22.5	30.6	30	18.5
1.0462	23.6	43	170.75	67.5	37.4	103.7	89.7	94.2	58.5	39	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	69.25	35.2	91.1	85.7	96.9	55.5	35.7	22	29.4	26.6	17.4
1.034	28.7	43	200.5	71.5	37.9	107.2	103.1	105.5	68.8	38.3	23.7	32.1	28.9	18.7
1.0854	6	44	184	74	37.9	100.8	89.1	102.6	60.6	39	24	32.9	29.2	18.4
1.0209	34.8	44	223	69.75	40.9	121.6	113.9	107.1	63.5	40.3	21.8	34.8	30.7	17.4
1.061	16.6	44	208.75	73	41.9	105.6	96.3	102	63.3	39.8	24.1	37.3	23.1	19.4
1.025	32.9	44	166	65.5	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	72.5	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	160.5	70.25	36	99.8	83.9	91.8	53	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	56	38.2	22.6	29	26.2	17.6
1.0829	7.1	49	140.5	68	35.8	91.2	79.4	89	51.1	35	21.7	30.9	28.8	17.4
1.0373	27.2	49	216.25	74.5	40.2	115.6	104	109	63.7	40.3	23.2	36.8	31	18.9
1.0543	19.5	49	168.25	71.75	38.3	98.3	89.7	99.1	56.3	38.8	23	29.5	27.9	18.6
1.0561	18.7	50	194.75	70.75	39	103.7	97.6	104.2	60	40.9	25.5	32.7	30	19
1.0543	19.5	50	172.75	73	37.4	98.7	87.6	96.1	57.1	38.1	21.8	28.6	26.7	18
0.995	47.5	51	219	64	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	154.5	70	36.9	93.3	81.5	94.4	54.7	39	22.6	27.5	25.9	18.6
1.0433	24.5	52	199.25	71.75	39.4	106.8	100	105	63.9	39.2	22.9	35.7	30.4	19.2
1.0646	15	53	154.5	69.25	37.6	93.9	88.7	94.5	53.7	36.2	22	28.5	25.7	17.1
1.0706	12.4	54	153.25	70.5	38.5	99	91.8	96.2	57.7	38.1	23.9	31.4	29.9	18.9
1.0399	26	54	230	72.25	42.5	119.9	110.4	105.5	64.2	42.7	27	38.4	32	19.6
1.0726	11.5	54	161.75	67.5	37.4	94.2	87.6	95.6	59.7	40.2	23.4	27.9	27	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
1.074	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	126.5	66.75	33.4	88.8	78.2	87.5	50.8	33	19.7	25.3	22	15.8
1.065	14.8	55	169.5	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	198.5	74.25	38.3	105.3	96.7	106.6	64	42.6	23.4	33.2	30	18.4
1.0647	14.9	56	174.5	69.5	38.1	104	89.4	98.4	58.4	37.4	22.5	34.6	30.1	18.8
1.0601	17	56	167.75	68.5	37.4	98.6	93	97	55.4	38.8	23.2	32.4	29.7	19
1.0745	10.6	57	147.75	65.75	35.2	99.6	86.4	90.1	53	35	21.3	31.7	27.3	16.9
1.062	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
1.0636	15.4	58	175.5	71.5	38	100.2	88.1	97.8	57.1	38.9	23.6	30.9	29.6	18
1.0384	26.7	58	161.75	67.25	35.1	94.9	94.9	100.2	56.8	35.9	21	27.8	26.1	17.6
1.0403	25.8	60	157.75	67.5	40.4	97.2	93.3	94	54.3	35.7	21	31.3	28.7	18.3
1.0563	18.6	62	168.75	67.5	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	191.5	72.25	40.6	104	98.2	101.1	59.3	40.3	23	32.6	28.5	19
1.0372	27.3	63	219.15	69.5	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	69.5	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	35.9	30.5	19.1
1.0599	17	65	127.5	65.75	34.7	93	79.7	87.6	50.7	33.4	20.1	28.5	24.8	16.5
1.0207	35	65	224.5	68.25	38.8	119.6	118	114.3	61.3	42.1	23.4	34.9	30.1	19.4
1.0304	30.4	66	234.25	72	41.4	119.7	109	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	25.4	35.3	29.8	19.5
1.0334	29	67	199.5	68.5	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	155.5	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	215.5	70.5	40.8	113.7	107.6	110	63.3	44	22.6	37.5	32.6	18.8
1.0736	11	70	134.25	67	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	69.75	40.9	108.5	105	104.5	59.6	40.8	23.2	35.2	28.6	20.1
1.0328	29.3	72	186.75	66	38.9	111.1	111.5	101.7	60.3	37.3	21.5	31.3	27.2	18
1.0399	26	72	190.75	70.5	38.9	108.3	101.3	97.8	56	41.6	22.7	30.5	29.4	19.8
1.0271	31.9	74	207.5	70	40.8	112.4	108.5	107.1	59.3	42.2	24.6	33.7	30	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