Garage Dings

One-car garages can be very small. Here is the driver's side wall of one such garage (thanks Laura). It displays the dings from opening the driver's side door in the tight space. Of course, the car is not parked in the same spot every time. Sometimes it rests a little farther forward in the garage and the door hits the wall more to the right in this image. Sometimes the car is parked just inside of the garage and the door dings fall on the left of this image. Most often the car is parked more centrally in the garage, leaving a greater frequency of door dings in the middle of the wall. This is a common pattern  on this blog: little wear on the left, much more in the middle, and then little wear on the right. This is the typical pattern of a bell-shaped, symmetric normal distribution, although any unimodal even roughly symmetric distribution could be described similarly.

Perhaps the wall needs a little tweak along these lines:

These are plots that highlight, with color, the highest density regions of a measurement, like the location of the door dings. The densities are estimated by the smooth curves. The measurements are shown by their random arrangement of tickmarks on the horizontal axes below the density curves - just like the garage door dings. These are the plots from Hyndman, R.J. (1996) "Computing and graphing highest density regions" American Statistician, 50, 120-126. These plots are one of many featured graphics in the R graph gallery.

Laura needs some blue, red, and green tape!