Articles in the media often report research results with a number, for example the number of hot flashes per day or the severity of menstrual cramps. However, these are not facts in the way that “man bites dog” would be a fact. In part, this is because the numbers in research reports often are averages. Averages are useful summaries, but they also leave out a lot of information. Take shoe size. If the average woman’s shoes are size 7, this does not mean that all women are size 7. It does not mean that a woman whose feet are size 8, 9, or 10 is abnormal or has a problem. At some point, a very large or small foot could mean that someone has a problem, but knowing where to draw the line requires knowing a lot more than the statistics. It means knowing something about the biology and biomechanics of feet. It means knowing about the context—for example, is a woman who wears a size 11 shoe five feet tall? or seven feet tall? This is different from a situation where numbers have an absolute meaning. For example, if my temperature is 102 degrees, then I have a fever, because of the realities of the biology of my body and not because of what most people’s average temperature is.
Image created by Paula Derry
What is an average? There are a few common ways of computing this. The median is the score for which half of the people being studied have higher scores and half lower. If the scores of all of the people being studied are added together and then divided by the number of people, this gives us the mean. The standard deviation is a number that indicates variation around the mean. If whatever is being measured has what is called a “normal distribution” (which is most often assumed) then over 68% of measurements will be within one standard deviation, and over 95% within two standard deviations of the mean.
Take osteoporosis and osteopenia. Osteoporosis is a bone disease that typically develops in old age in which bone is fragile and more likely to fracture [pdf]. This has been defined as a bone density measurement that is more than 2.5 standard deviations below that of an average 30-year-old woman. Osteopenia is having bone density that is not thin enough to be osteoporosis, but thinner than “normal,” and is defined as bone density 1-2.5 standard deviations below that of a 30-year-old woman. These definitions are statistical, i.e., different from an average (young) woman. Sometimes women are told that they have bone disease based on these definitions. With regard to osteopenia, the assumption is that this is an early stage of disease that will get worse over time and become osteoporosis. Sometimes women with osteopenia are advised to use a medication to prevent the disease progressing. However, these statistical definitions have been controversial. For example, other doctors assert that it is normal for bone to thin as women age and that only a small percentage of women with osteopenia go on to get osteoporosis. Some doctors believe that a diagnosis of osteoporosis itself requires more than low bone density—for example, that a woman has had a bone fracture or that other indications exist.
Or take the number of days in the normal menstrual cycle. The stereotype is that the average menstrual cycle is 28 days long and that regularly recurring cycles are what is healthy. A study published in 1967 by Treloar and colleagues presents some of the complexities that this stereotype ignores. Assuming that there is one average menstrual cycle length for all women leaves out important information about changes that occur over time, across a woman’s adult life. The average cycle length when a large group of women were studied was indeed 28 to 26 days (median length). However, this was for women aged 20-40. During the first few years after menarche and the last few years before menopause, median cycle length was over 30 days. Even more striking is the amount of variability from one woman to the next, and how this variability changes over time. Among 20-year-old women, for example, the cycle could be anywhere from 24 to 38 days, or occasionally less or more. However, the first year that periods began, these differences between women were larger—cycle length was between 18 and 83 days. Variability between women decreased for about eight years, but, as I have said, even when women were most similar (at ages 20-40) there were still big differences among them. Variability increased again about eight years before menopause; the last year before menopause, women had cycle lengths from 18 to 80 days. An individual woman’s cycle lengths changed over her life span; further, cycle lengths varied from month to month as well as over a span of years in ways that were very different for different women.
Averages have useful information. However, it’s always important to know what the numbers mean in order to interpret them. This is important for knowing what an average means, and it’s always important to remember that an individual’s reality may be very different from the picture derived from finding an average for a large group of people.
