## Wednesday, 2 March 2011

### Normally Distributed

Another nice statistical curiosity from the Statpics blog of Professor Robert Jernigan at American University.  The entire short post is copied below, and I would love to hear responses to the final question.  And it also looks like the wear on the left door is distinctly heavier than the right..do you agree? and if it is...why?  Do we go out with our left and in with our right, or ??? Anyway, here is the Professor's blog:
------------------------------------------------------------------------------------
An image of the wear on exit doors at a Barnes and Noble bookstore in Rockville, Maryland. Most wear is located a little below shoulder height as customers push on the door with outstretched arms as they exit. Or are they holding open the door with fingers as they enter? It turns out it's both. (Yes, I stood there and watched!). It's both uncomfortable and inefficient to open the door much higher or much lower. We're left with a greater frequency of use centrally located with less and less wear above and below: a unimodal frequency distribution of wear. Considering that human height is approximately normally distributed, the patterns here should reflect that normality. It's interesting to note that the left hand door seems to have a frequency distribution of wear that sits slightly above that for the right hand door.
Any ideas as to why?
-----------------------------------------
Addendum: MLB sent a comment with a couple of ideas that were too perfect to leave in the comments.  Another cool place where a similar unimodal distribution pattern shows up is on Jerusalem's Western Wall:

Finally, this phenomenon is the reason why these sort of locks are unsafe:  One time I was with a group of people locked out of a building. A member of our group had left something inside, and none of us had a key. There was a lock box, though, and some careful observation of the exterior of the box gave us some good guesses as to the combination. We got in without trouble.