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Chapter 1. Height and weight

Useful Calculations

Useful Calculations

The purpose of this work is to promote fluency in the language of mathematics among students who have had little experience (or perhaps an unpleasant experience) with standard math courses. Every educated person needs to become "numerate", not only to solve practical problems, but also to develop paths of communication with scientists, physicians, and engineers, whose work requires that they think in a quantitative manner.

BMI Calculation

Young adults of the human species grow to a certain height, then cease to grow. Body weight, however, can be controlled, within limits. A slender body, apart from looking good in clothing (and without) confers a definite health advantage, according to several long-term studies. Life insurance companies have known for at least 50 years that thinner people have lower mortality rates. A 1959 table of desirable weights for particular heights shows that, for example, a woman 155 cm (centimeters) tall should weigh no more than 48.5 kg (kilograms). These dimensions are equal to 5 feet 1 inch and 107 pounds. Modifications of such tables are still published, but since 1990, health professionals have used body-mass-index (BMI), which is in units of kilograms per square meter.

If your bathroom scale lacks read-out in kilograms, you can either (1) buy a new scale, or (2) use your calculator to divide your weight in pounds by the conversion factor 2.20462 pounds per kg. Thus your weight in kg is less than half your weight in pounds, and you have already made progress in your weight-loss program. No, not really, but you are getting better at arithmetic. To convert 154.3 lbs to kg:

154.3 lbs / 2.20462 = 70.0 kg

The 70-kg man was once the standard in medical physiology, probably because medical students were a good source of human subjects for testing, and they were all young males of average weight and height.

The next step in calculating the BMI is either (1) to measure the person's height in meters, or (2) to convert inches to meters by dividing inches by 39.37 in/m. For example, a person exactly 5 feet 8 inches tall:

68.0 in / 39.37 = 1.727 m

In a class exercise, 37 female college students reported an average height of 1.635 meters , and 16 male students reported 1.792 m. If your height differs greatly from these, check your calculation.

Now, one must square the height, which is done easily by entering the number, and pressing the x2 button:

(1.727 m)2 = 2.9825 m2.

And the final step is:

70.0 kg / 2.9825 m2 = 23.5 kg/m2 = BMI

A healthy BMI falls between 18.5 and 24.9 kg/m2. Numbers from 25 to 29.9 indicate overweight, and a BMI greater than 30 indicates obesity. However, some athletes have BMI greater than 30, because of greater muscle mass, and they are not considered unhealthy.

Rounding

In calculations of this sort, the number of figures in the original data determines the number in the result, and the rule is to use all the figures available, and round off in the final step. With three significant figures, a number such as 20.06 is rounded up to 20.1, and 20.04 is rounded down to 20.0. If the last number to the right is 5, one rounds to the nearest even number; thus both 20.15 and 20.25 become 20.2 when rounded, and bias is avoided.

Exercise 1. Get accurate measurements of your weight and height, and calculate your body mass index. Convert the data in Table 1 to metric units, calculate BMI for each man, and classify them as normal, overweight, or obese.

Table 1. Dimensions of selected individuals.
HT (ft. - in.) WT (1bs)
Robert P. Wadlow, circus giant 8 - 11.1 490
Manute Bol, NBA center 7 - 6.75 225
Haile Gebrselassie, runner 5 - 3 119
William Klinke, jockey 4 - 3 103

BMI and Health

Health experts agree that a combination of more exercise and less intake of fatty foods is needed to combat obesity. The importance of maintaining a healthy weight in order to reduce health risks has been well publicized.

Increases in BMI with age have been observed often, but they are apparently not inevitable. Increases in BMI during pregnancy are inevitable, because the average full-term baby weighs 3.40 kg, and the placenta and fluids weigh 6.80 kg. The physician allows a woman with normal BMI to gain 10.20 kg during pregnancy. In his newspaper column of 23 January 2002, Dr. Paul G. Donohue recommended that a woman with BMI less than 19.8 kg/m2 be allowed to gain more than 10 kg, and a woman with BMI above 26 be advised to limit weight gain to 9 kg or less.

Another ratio, suggested by diet and nutrition writers, supplements the BMI. The circumference or distance around the waist is compared with the like measurement of the hips. The ratio waist/hip should be less than 0.80 for women, and less than 0.95 for men. For example: 86cm / 96cm = 0.90 is OK for a man. A healthy woman is expected to have a smaller waistline.

Vive la difference.