-What is the mean of 1 and 23 ?
-Well, 12 of course.
-So if one day you go to sleep at 23 o'clock (11pm), the other day at 1am, what was your average go-to-sleep time ?
-12 (noon)? NO! 0 (midnight).
Turns out that the mean of circular quantities (hours, spatial directions, etc.) is trickier than seems at first, and involves a bit of trigonometry or at least the use of complex numbers.
http://en.wikipedia.org/wiki/Directional_statistics
http://en.wikipedia.org/wiki/Mean_of_circular_quantities
2.
I wish it was a joke:
Medical researcher reinvents trapezoidal method for integration in 1994, paper gets cited 80+ times. Something rotten in the state of medical research:
http://care.diabetesjournals.org/content/17/2/152.abstract
From the paper:
"A mathematical model for the determination of total area under glucose tolerance and other metabolic curves."
"OBJECTIVE--To develop a mathematical model for the determination of total areas under curves from various metabolic studies. RESEARCH DESIGN AND METHODS--In Tai's Model, the total area under a curve is computed by dividing the area under the curve between two designated values on the X-axis (abscissas) into small segments (rectangles and triangles) whose areas can be accurately calculated from their respective geometrical formulas. The total sum of these individual areas thus represents the total area under the curve. Validity of the model is established by comparing total areas obtained from this model to these same areas obtained from graphic method (less than +/- 0.4%). Other formulas widely applied by researchers under- or overestimated total area under a metabolic curve by a great margin."
via: http://www.reddit.com/r/math/comments/eero3/1
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