Body mass index

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A graph of body mass index as a function of body mass and body height is shown above. The dashed lines represent subdivisions within a major class. For instance the "Underweight" classification is further divided into "severe", "moderate", and "mild" subclasses.[1]

The body mass index (BMI), or Quetelet index, is a measure for human body shape based on an individual's weight and height. It was devised between 1830 and 1850 by the Belgian polymath Adolphe Quetelet during the course of developing "social physics".[2] Body mass index is defined as the individual's body mass divided by the square of their height. The formulae universally used in medicine produce a unit of measure of kg/m2. BMI can also be determined using a BMI chart,[3] which displays BMI as a function of weight (horizontal axis) and height (vertical axis) using contour lines for different values of BMI or colors for different BMI categories.

\mathrm{BMI} = \frac{\text{mass}(\text{kg})}{\left(\text{height}(\text{m})\right)^2}
 
= \frac{\text{mass}(\text{lb})}{\left(\text{height}(\text{in})\right)^2}\times 703 

The factor for UK/US units is more precisely 703.06957964, but that level of precision is not meaningful for this calculation. To work from stone and pounds first multiply the stone by 14 then add the pounds to give the whole mass in pounds; to work from feet and inches first multiply the feet by 12 then add the inches to give the whole height in inches.

Contents

Usage[edit]

While the formula previously called the Quetelet Index for BMI dates to the 19th century, the new term "body mass index" for the ratio and its popularity date to a paper published in the July edition of 1972 in the Journal of Chronic Diseases by Ancel Keys, which found the BMI to be the best proxy for body fat percentage among ratios of weight and height;[4][5] the interest in measuring body fat being due to obesity becoming a discernible issue in prosperous Western societies. BMI was explicitly cited by Keys as being appropriate for population studies, and inappropriate for individual diagnosis. Nevertheless, due to its simplicity, it came to be widely used for individual diagnosis, despite its inappropriateness.

BMI provided a simple numeric measure of a person's thickness or thinness, allowing health professionals to discuss overweight and underweight problems more objectively with their patients. However, BMI has become controversial because many people, including physicians, have come to rely on its apparent numerical authority for medical diagnosis, but that was never the BMI's purpose; it is meant to be used as a simple means of classifying sedentary (physically inactive) individuals, or rather, populations, with an average body composition.[6] For these individuals, the current value settings are as follows: a BMI of 18.5 to 25 may indicate optimal weight; a BMI lower than 18.5 suggests the person is underweight while a number above 25 may indicate the person is overweight; a person may have a BMI below 18.5 due to disease; a number above 30 suggests the person is obese (over 40, morbidly obese).

For a given height, BMI is proportional to mass. However, for a given mass, BMI is inversely proportional to the square of the height. So, if all body dimensions double, and mass scales naturally with the cube of the height, then BMI doubles instead of remaining the same. This results in taller people having a reported BMI that is uncharacteristically high compared to their actual body fat levels. In comparison, the Ponderal index is based on this natural scaling of mass with the third power of the height. However, many taller people are not just "scaled up" short people, but tend to have narrower frames in proportion to their height. Nick Korevaar (a mathematics lecturer from the University of Utah) suggests that instead of squaring the body height (an exponent of 2, as the BMI does) or cubing the body height (an exponent of 3, as the Ponderal index does), it would be more appropriate to use an exponent of between 2.3 and 2.7[7] (as originally noted by Quetelet). (For a theoretical basis for such values see MacKay.[8])

BMI Prime[edit]

BMI Prime, a simple modification of the BMI system, is the ratio of actual BMI to upper limit BMI (currently defined at BMI 25). As defined, BMI Prime is also the ratio of body weight to upper body weight limit, calculated at BMI 25. Since it is the ratio of two separate BMI values, BMI Prime is a dimensionless number, without associated units. Individuals with BMI Prime less than 0.74 are underweight; those between 0.74 and 1.00 have optimal weight; and those at 1.00 or greater are overweight. BMI Prime is useful clinically because individuals can tell, at a glance, by what percentage they deviate from their upper weight limits. For instance, a person with BMI 34 has a BMI Prime of 34/25 = 1.36, and is 36% over his or her upper mass limit. In South East Asian and South Chinese populations (see international variation section below) BMI Prime should be calculated using an upper limit BMI of 23 in the denominator instead of 25. Nonetheless, BMI Prime allows easy comparison between populations whose upper limit BMI values differ.[9]

Categories[edit]

A frequent use of the BMI is to assess how much an individual's body weight departs from what is normal or desirable for a person of his or her height. The weight excess or deficiency may, in part, be accounted for by body fat (adipose tissue) although other factors such as muscularity also affect BMI significantly (see discussion below and overweight). The WHO regards a BMI of less than 18.5 as underweight and may indicate malnutrition, an eating disorder, or other health problems, while a BMI greater than 25 is considered overweight and above 30 is considered obese.[10] These ranges of BMI values are valid only as statistical categories

CategoryBMI range – kg/m2BMI Prime
Very severely underweightless than 15less than 0.60
Severely underweightfrom 15.0 to 16.0from 0.60 to 0.64
Underweightfrom 16.0 to 18.5from 0.64 to 0.74
Normal (healthy weight)from 18.5 to 25from 0.74 to 1.0
Overweightfrom 25 to 30from 1.0 to 1.2
Obese Class I (Moderately obese)from 30 to 35from 1.2 to 1.4
Obese Class II (Severely obese)from 35 to 40from 1.4 to 1.6
Obese Class III (Very severely obese)over 40over 1.6

BMI-for-age[edit]

BMI for age percentiles for boys 2 to 20 years of age.

BMI is used differently for children. It is calculated the same way as for adults, but then compared to typical values for other children of the same age. Instead of set thresholds for underweight and overweight, then, the BMI percentile allows comparison with children of the same sex and age.[11] A BMI that is less than the 5th percentile is considered underweight and above the 95th percentile is considered obese for people 20 and under. People under 20 with a BMI between the 85th and 95th percentile are considered to be overweight.

Recent studies in Britain have indicated that females between the ages 12 and 16 have a higher BMI than males of the same age by 1.0 kg/m2 on average.[12]

International variations[edit]

These recommended distinctions along the linear scale may vary from time to time and country to country, making global, longitudinal surveys problematic.

United States[edit]

In 1998, the U.S. National Institutes of Health and the Centers for Disease Control and Prevention brought U.S. definitions into line with World Health Organization guidelines, lowering the normal/overweight cut-off from BMI 27.8 to BMI 25. This had the effect of redefining approximately 29 million Americans, previously healthy to overweight.[13] It also recommends lowering the normal/overweight threshold for South East Asian body types to around BMI 23, and expects further revisions to emerge from clinical studies of different body types.

The U.S. National Health and Nutrition Examination Survey of 1994 indicated that 59% of American men and 49% of women had BMIs over 25. Morbid obesity—a BMI of 40 or more—was found in 2% of the men and 4% of the women. The newest survey in 2007 indicates a continuation of the increase in BMI: 63% of Americans are overweight or obese, with 26% now in the obese category (a BMI of 30 or more). There are differing opinions on the threshold for being underweight in females; doctors quote anything from 18.5 to 20 as being the lowest index, the most frequently stated being 19. A BMI nearing 15 is usually used as an indicator for starvation and the health risks involved, with a BMI less than 17.5 being an informal criterion for the diagnosis of anorexia nervosa.

Japan[edit]

Japan Society for the Study of Obesity(2000)[14]

CategoryBMI range – kg/m2
Low18.5 and below
Normalfrom 18.5 to 25.0 (Standard weight is 22)
Obese (Level 1)from 25.0 to 30.0
Obese (Level 2)from 30.0 to 35.0
Obese (Level 3)from 35.0 to 40.0
Obese (Level 4)40.0 and above

[15][clarification needed]

Singapore[edit]

In Singapore, the BMI cut-off figures were revised in 2005, motivated by studies showing that many Asian populations, including Singaporeans, have higher proportion of body fat and increased risk for cardiovascular diseases and diabetes mellitus, compared with Caucasians at the same BMI. The BMI cut-offs are presented with an emphasis on health risk rather than weight.[16]

BMI range – kg/m2Health Risk
27.5 and aboveHigh risk of developing heart disease, high blood pressure, stroke, diabetes
23.0 to 27.4Moderate risk of developing heart disease, high blood pressure, stroke, diabetes
18.5 to 22.9Low Risk (healthy range)
18.4 and belowRisk of developing problems such as nutritional deficiency and osteoporosis

Health consequences of overweight and obesity in adults[edit]

The BMI ranges are based on the relationship between body weight and disease and death.[17] Overweight and obese individuals are at increased risk for many diseases and health conditions, including the following:[18]

Applications[edit]

Statistical device[edit]

The BMI is generally used as a means of correlation between groups related by general mass and can serve as a vague means of estimating adiposity. The duality of the BMI is that, whilst easy-to-use as a general calculation, it is limited in how accurate and pertinent the data obtained from it can be. Generally, the index is suitable for recognizing trends within sedentary or overweight individuals because there is a smaller margin for errors.[19]

This general correlation is particularly useful for consensus data regarding obesity or various other conditions because it can be used to build a semi-accurate representation from which a solution can be stipulated, or the RDA for a group can be calculated. Similarly, this is becoming more and more pertinent to the growth of children, due to the majority of their exercise habits.[20]

The growth of children is usually documented against a BMI-measured growth chart. Obesity trends can be calculated from the difference between the child's BMI and the BMI on the chart.[citation needed]

Clinical practice[edit]

BMI has been used by the WHO as the standard for recording obesity statistics since the early 1980s. In the United States, BMI is also used as a measure of underweight, owing to advocacy on behalf of those suffering with eating disorders, such as anorexia nervosa and bulimia nervosa.[citation needed]

BMI can be calculated quickly and without expensive equipment. However, BMI categories do not take into account many factors such as frame size and muscularity.[19] The categories also fail to account for varying proportions of fat, bone, cartilage, water weight, and more.[citation needed]

Despite this, BMI categories are regularly regarded as a satisfactory tool for measuring whether sedentary individuals are underweight, overweight or obese with various exemptions, such as: athletes, children, the elderly, and the infirm.[citation needed]

One basic problem, especially in athletes, is that muscle weight contributes to BMI. Some professional athletes would be overweight or obese according to their BMI, despite carrying little fat, unless the number at which they are considered overweight or obese is adjusted upward in some modified version of the calculation.[citation needed] In children and the elderly, differences in bone density and, thus, in the proportion of bone to total weight can mean the number at which these people are considered underweight should be adjusted downward.[citation needed]

Medical underwriting[edit]

In the United States, where medical underwriting of private health insurance plans is widespread, most private health insurance providers will use a particular high BMI as a cut-off point in order to raise insurance rates for or deny insurance to higher-risk patients, thereby reducing the cost of insurance coverage to all other subscribers in a lower BMI range. The cutoff point is determined differently for every health insurance provider and different providers will have vastly different ranges of acceptability. Many will implement phased surcharges, in which the subscriber will pay an additional penalty, usually as a percentage of the monthly premium, based on membership in an actuarially determined risk tier corresponding to a given range of BMI points above a certain acceptable limit, up to a maximum BMI past which the individual will simply be denied admissibility regardless of price. This can be contrasted with group insurance policies which do not require medical underwriting and where insurance admissibility is guaranteed by virtue of being a member of the insured group, regardless of BMI or other risk factors that would likely render the individual inadmissible to an individual health plan.[citation needed]

Limitations and shortcomings[edit]

This graph shows the correlation between body mass index (BMI) and percent body fat (%BF) for 8550 men in NCHS' NHANES 1994 data. Data in the upper left and lower right quadrants show some limitations of BMI.[21]

The medical establishment has acknowledged major shortcomings of BMI.[22] Because the BMI formula depends only upon weight and height, its assumptions about the distribution between lean mass and adipose tissue are inexact. BMI generally overestimates adiposity on those with more lean body mass (e.g. athletes) and underestimates excess adiposity on those with less lean body mass. A study in June, 2008 by Romero-Corral et al. examined 13,601 subjects from the United States' third National Health and Nutrition Examination Survey (NHANES III) and found that BMI-defined obesity (BMI > 30) was present in 21% of men and 31% of women. Using body fat percentages (BF%), however, BF%-defined obesity was found in 50% of men and 62% of women. While BMI-defined obesity showed high specificity (95% for men and 99% for women), BMI showed poor sensitivity (36% for men and 49% for women). Despite this undercounting of obesity by BMI, BMI values in the intermediate BMI range of 20-30 were found to be associated with a wide range of body fat percentages. For men with a BMI of 25, about 20% have a body fat percentage below 20% and about 10% have body fat percentage above 30%.[21]

Mathematician Keith Devlin and a restaurant industry association The Center for Consumer Freedom argue that the error in the BMI is significant and so pervasive that it is not generally useful in evaluation of health.[23][24] University of Chicago political science professor Eric Oliver says BMI is a convenient but inaccurate measure of weight, forced onto the populace, and should be revised.[25]

A study published by JAMA in 2005 showed that overweight people had a similar relative risk of mortality to normal weight people as defined by BMI, while underweight and obese people had a higher death rate.[26] High BMI is associated with type 2 diabetes only in persons with high serum gamma-glutamyl transpeptidase.[27]

In an analysis of 40 studies involving 250,000 people, patients with coronary artery disease with normal BMIs were at higher risk of death from cardiovascular disease than people whose BMIs put them in the overweight range (BMI 25–29.9).[28] In the overweight, or intermediate, range of BMI (25–29.9), the study found that BMI failed to discriminate between bodyfat percentage and lean mass. The study concluded that "the accuracy of BMI in diagnosing obesity is limited, particularly for individuals in the intermediate BMI ranges, in men and in the elderly. These results may help to explain the unexpected better survival in overweight/mild obese patients."[21]

A 2010 study that followed 11,000 subjects for up to eight years concluded that BMI is not a good measure for the risk of heart attack, stroke or death. A better measure was found to be the waist-to-height ratio.[29] However, a 2011 study that followed 60,000 participants for up to 13 years found that waist–hip ratio was a better predictor of ischaemic heart disease mortality.[30]

BMI is particularly inaccurate for people who are fit or athletic, as the higher muscle mass tends to put them in the overweight category by BMI, even though their body fat percentages frequently fall in the 10–15% category, which is below that of a more sedentary person of average build who has a normal BMI number. Body composition for athletes is often better calculated using measures of body fat, as determined by such techniques as skinfold measurements or underwater weighing and the limitations of manual measurement have also led to new, alternative methods to measure obesity, such as the body volume index. However, recent studies of American football linemen who undergo intensive weight training to increase their muscle mass show that they frequently suffer many of the same problems as people ordinarily considered obese, notably sleep apnea.[31][32]

BMI also does not account for body frame size; a person may have a small frame and be carrying more fat than optimal, but their BMI reflects that they are normal. Conversely, a large framed individual may be quite healthy with a fairly low body fat percentage, but be classified as overweight by BMI. Accurate frame size calculators use several measurements (wrist circumference, elbow width, neck circumference and others) to determine what category an individual falls into for a given height. The standard is to use frame size in conjunction with ideal height/weight charts and add roughly 10% for a large frame or subtract roughly 10% for a smaller frame.[citation needed]

For example, a chart may say the ideal weight for a man 5'10" (178 cm) is 165 pounds (75 kg). But if that man has a slender build (small frame), he may be overweight at 165 pounds (75 kg) and should reduce by 10%, to roughly 150 pounds (68 kg). In the reverse, the man with a larger frame and more solid build can be quite healthy at 180 pounds (82 kg). If one teeters on the edge of small/medium or medium/large, a dose of common sense should be used in calculating their ideal weight. However, falling into your ideal weight range for height and build is still not as accurate in determining health risk factors as waist/height ratio and actual body fat percentage.

A further limitation of BMI relates to loss of height through aging. In this situation, BMI will increase without any corresponding increase in weight.

The exponent of 2 in the denominator of the formula for BMI is arbitrary. It is meant to reduce variability in the BMI associated only with a difference in size, rather than with differences in weight relative to one's ideal weight. If taller people were simply scaled-up versions of shorter people, the appropriate exponent would be 3, as weight would increase with the cube of height. However, on average, taller people have a slimmer build relative to their height than do shorter people, and the exponent which matches the variation best is between 2 and 3. An analysis based on data gathered in the USA suggested an exponent of 2.6 would yield the best fit for children aged 2 to 19 years old.[33] The exponent 2 is used instead by convention and for simplicity.

As a possible alternative to BMI, the concepts fat-free mass index (FFMI) and fat mass index (FMI) were introduced in the early 1990s.[34]

Varying standards[edit]

It is not clear where on the BMI scale the threshold for overweight and obese should be set. Because of this the standards have varied over the past few decades. Between 1980 and 2000 the U.S. Dietary Guidelines have defined overweight at a variety of levels ranging from a BMI of 24.9 to 27.1. In 1985 the National Institutes of Health (NIH) consensus conference recommended that overweight BMI be set at a BMI of 27.8 for men and 27.3 for women. In 1988 a NIH report concluded that a BMI over 25 is overweight and a BMI over 30 is obese. In the 1990s the World Health Organization (WHO) decided that a BMI of 25 to 30 should be considered overweight and a BMI over 30 is obese, the standards the NIH set. This became the definitive guide for determining if someone is overweight.

The current WHO and NIH ranges of normal weights are proved to be associated with decreased risks of some diseases such as diabetes type II ; however using the same range of BMI for men and women is considered arbitrary, and makes the definition of underweight quite unsuitable for men.[35]

Global statistics[edit]

Researchers at the London School of Hygiene & Tropical Medicine calculated the average BMI for 177 countries using UN data on population, WHO estimates of global weight, and mean height from national health examination surveys.[36]

See also[edit]

Other measures of obesity:

References[edit]

  1. ^ "BMI classification". Global Database on Body Mass Index. WHO. 2006. Retrieved July 27, 2012. 
  2. ^ Eknoyan, Garabed (2007). "Adolphe Quetelet (1796–1874)—the average man and indices of obesity". Nephrology Dialysis Transplantation 23 (1): 47–51. doi:10.1093/ndt/gfm517. PMID 17890752. 
  3. ^ E.g., the Body Mass Index Table from the National Institutes of Health's NHLBI.
  4. ^ Beyond BMI: Why doctors won't stop using an outdated measure for obesity., by Jeremy Singer-Vine, Slate.com, July 20, 2009
  5. ^ Keys, Ancel; Fidanza, Flaminio; Karvonen, Martti J.; Kimura, Noboru; Taylor, Henry L. (1972). "Indices of relative weight and obesity". Journal of Chronic Diseases 25 (6–7): 329–43. doi:10.1016/0021-9681(72)90027-6. PMID 4650929. 
  6. ^ "Physical Status: The Use and Interpretation of Anthropometry". WHO Technical Report Series 854: 9. 
  7. ^ Korevaar, Nick (July 2003). "Notes on Body Mass Index and actual national data". [self-published source?][unreliable medical source?]
  8. ^ MacKay, N.J. (2010). "Scaling of human body mass with height: The body mass index revisited". Journal of Biomechanics 43 (4): 764–6. arXiv:0910.5834. Bibcode:2009arXiv0910.5834M. doi:10.1016/j.jbiomech.2009.10.038. PMID 19909957. 
  9. ^ Gadzik, James (2006). "'How much should I weigh?' Quetelet's equation, upper weight limits, and BMI prime". Connecticut Medicine 70 (2): 81–8. PMID 16768059. 
  10. ^ "BMI Classification". World Health Organization. 
  11. ^ "Body Mass Index: BMI for Children and Teens". Center for Disease Control. 
  12. ^ "Health Survey for England: The Health of Children and Young People". 
  13. ^ "Who's fat? New definition adopted". CNN. Retrieved 2010-04-26. 
  14. ^ "肥満って、 どんな状態?". 肥満ホームページ. 厚生労働省. Retrieved 2013-05-25. 
  15. ^ Shiwaku, K; Anuurad, E; Enkhmaa, B; Nogi, A; Kitajima, K; Shimono, K; Yamane, Y; Oyunsuren, T (2003). "Overweight Japanese with body mass indexes of 23.0–24.9 have higher risks for obesity-associated disorders: A comparison of Japanese and Mongolians". International Journal of Obesity 28 (1): 152–8. doi:10.1038/sj.ijo.0802486. PMID 14557832. 
  16. ^ "Revision of Body Mass Index (BMI) Cut-Offs In Singapore". 
  17. ^ World Health Organization. Physical status: The use and interpretation of anthropometry. Geneva, Switzerland: World Health Organization 1995. WHO Technical Report Series.
  18. ^ "Executive Summary". Clinical Guidelines on the Identification, Evaluation, and Treatment of Overweight and Obesity in Adults: The Evidence Report. National Heart, Lung, and Blood Institute. September 1998. xi–xxx. 
  19. ^ a b Jeukendrup, A.; Gleeson, M. (2005). Sports Nutrition. Human Kinetics: An Introduction to Energy Production and Performance. ISBN 978-0-7360-3404-3. [page needed]
  20. ^ Barasi, M. E. (2004). Human Nutrition - a health perspective. ISBN 0-340-81025-4. [page needed]
  21. ^ a b c Romero-Corral, A; Somers, V K; Sierra-Johnson, J; Thomas, R J; Collazo-Clavell, M L; Korinek, J; Allison, T G; Batsis, J A et al. (2008). "Accuracy of body mass index in diagnosing obesity in the adult general population". International Journal of Obesity 32 (6): 959–66. doi:10.1038/ijo.2008.11. PMC 2877506. PMID 18283284. 
  22. ^ "Aim for a Healthy Weight: Assess your Risk". National Institutes of Health. 2007-07-08. 
  23. ^ "Do You Believe in Fairies, Unicorns, or the BMI?". Mathematical Association of America. 2009-05-01. Retrieved 2009-05-22. 
  24. ^ "Is obesity such a big, fat threat?". Cox News Service. 2004-08-30. Archived from the original on 2007-08-04. Retrieved 2007-07-08. 
  25. ^ Sheldon, Linzi (April 26, 2005). "Oliver blames 'obesity mafia' for American weight scare". The Dartmouth. 
  26. ^ Flegal, K. M.; Graubard, BI; Williamson, DF; Gail, MH (2005). "Excess Deaths Associated with Underweight, Overweight, and Obesity". JAMA 293 (15): 1861–7. doi:10.1001/jama.293.15.1861. PMID 15840860. 
  27. ^ Lim JS, Lee DH, Park JY, Jin SH, Jacobs DR Jr (2007). "A strong interaction between serum gamma-glutamyltransferase and obesity on the risk of prevalent type 2 diabetes: results from the Third National Health and Nutrition Examination Survey". CLINICAL CHEMISTRY 53 (6): 1092–1098. doi:10.1016/j.jacl.2011.05.004. PMID 17478563. 
  28. ^ Romero-Corral, Abel; Montori, Victor M; Somers, Virend K; Korinek, Josef; Thomas, Randal J; Allison, Thomas G; Mookadam, Farouk; Lopez-Jimenez, Francisco (2006). "Association of bodyweight with total mortality and with cardiovascular events in coronary artery disease: A systematic review of cohort studies". The Lancet 368 (9536): 666–78. doi:10.1016/S0140-6736(06)69251-9. PMID 16920472. 
  29. ^ Schneider, H. J.; Friedrich, N.; Klotsche, J.; Pieper, L.; Nauck, M.; John, U.; Dorr, M.; Felix, S. et al. (2010). "The Predictive Value of Different Measures of Obesity for Incident Cardiovascular Events and Mortality". Journal of Clinical Endocrinology & Metabolism 95 (4): 1777–85. doi:10.1210/jc.2009-1584. PMID 20130075. 
  30. ^ Mørkedal, Bjørn; Romundstad, Pål R; Vatten, Lars J. (2011). "Informativeness of indices of blood pressure, obesity and serum lipids in relation to ischaemic heart disease mortality: the HUNT-II study". European Journal of Epidemiology 26 (6): 457–461. doi:10.1007/s10654-011-9572-7. ISSN 0393-2990. PMID 21461943. 
  31. ^ Brown, David (January 23, 2003). "Linemen More Likely To Have Sleep Condition". The Washington Post. 
  32. ^ Reinberg, Steven (January 29, 2007). "Ex-NFL Linemen prone to Heart Disease". The Washington Post. Retrieved 2010-04-26. 
  33. ^ "Power law fit to USA weight and height data". 
  34. ^ Vanitallie, TB; Yang, MU; Heymsfield, SB; Funk, RC; Boileau, RA (1990). "Height-normalized indices of the body's fat-free mass and fat mass: Potentially useful indicators of nutritional status". The American journal of clinical nutrition 52 (6): 953–9. PMID 2239792. 
  35. ^ "About the 'Medical Recommendation' of Ideal Weight". 2010-12-18. 
  36. ^ Data extracted from BBC News - Where are you on the global fat scale?
  37. ^ Assuming equal male and female population (generally correct within 5%)

Further reading[edit]

External links[edit]