Tutoring statistics, questions arise from it.  The tutor begins a discussion about some recent findings.

Twenty years ago I sold suits.  A good deal of customers had 38″ or 40″ waists.  However, there were more men smaller than that, rather than bigger; I would have thought the average to be, at most, 38″.

According to the CDC, the average waist size of males 20 years and over in the US, years 2007-2010, was 100.9cm (39.7″, but the report is in cm).  They acknowledge that waist sizes have increased, so perhaps their findings fit with my recollections.

What is perhaps even more interesting about the CDC report is the distribution of their data. They claim the standard error of the mean to be 0.41, with sample size 5410. By definition, the standard error of the mean is σ/√n.  Therefore, if we multiply the standard error of the mean by the square root of the sample size, we arrive at the sample standard deviation.  With the square root of 5410 being 73.55, the sample standard deviation should be 0.41×73.55=30.2 cm.

With the normal distribution, the 16th percentile occurs at one standard deviation below the mean.  Therefore, with mean waistline 100.9cm, and standard deviation 30.2cm, one would likely expect the 16th percentile to be approximately 70.7 cm (100.9-30.2).  However, the report puts the 15th percentile at 85.4 – about half a standard deviation below the mean.  I’d call this atypical of a normal distribution.

The average adult male waistline being 39.7″, along with the unexpected distribution of the data:  both points invite follow-up in future posts:)

Sources:

Harnett, Donald and James Murphy. Statistical Analysis for Business and Economics.    Don Mills: Addison-Wesley, 1986.

cdc.gov

Jack of Oracle Tutoring by Jack and Diane, Cambpell River, BC.