“The serum total cholesterol for males 20–29 years old is approximately normally distributed with mean m = 180 and s = 36.2, based on data obtained from the National Health and Nutrition Examination Survey… An individual with total cholesterol greater than 200 is considered to have high cholesterol…The area under the normal curve to the right of x = 200 is 0.2903.”
Sullivan III, Michael. Statistics: Informed Decisions Using Data (Page 362). Pearson Education. Kindle Edition.
Is this not shocking? 29% of males 20-29 years old have high cholesterol, yet the cutoff score of 200 is not even one standard deviation above the mean, and thus this analysis is treating 29% of these young men as “outliers” – people needing treatment, when common sense says that it is likely that only real outliers (for a normal distribution an outlier is defined such that it is either <= or >= 2.7 standard deviations above the mean) should need treatment.
Or is the pharmaceutical industry correct? Is high blood cholesterol really that intrinsically dangerous?
An analogy: the average IQ is 100 and the standard deviation is 15. A person with an IQ of 110 is less than 1 standard deviation above the mean. Would it be wise to put a child with an IQ of 110 in a class of obvious outliers, aka a class for “gifted children”? I think it would be silly. Is treating young men with statins because their cholesterol is 200 not just as silly? Maybe, maybe not.
When are we going to let the term “outliers” stand for what it is – extremely rare individuals, who if brilliant, need to be in a class for gifted children, and who if possessed of an extremely high cholesterol, may need to be treated with drugs for their own safety.