## Tuesday, March 1, 2011

### Matching Normal Densities

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?

#### 6 comments:

Eric Tramel said...

Are left handed people any taller on average?

Or, perhaps, the right door represents the majority of people (i.e. right handers) exiting, while the left handed door is more representative of entrance finger-grabs. Do people tend to finger-grab higher than they push?

I would think this would be true. Late initiation of an exiting push would create a lower hit on the door since the arm would only be half extended.

A finger-grab on an entrance would mean that an arm would be more or less outstretched, creating a higher door hit.

math233 said...

Pictures of worn wooden steps with the middle more worn down than the sides would probably be another example of a (upside down) normal distribution. J.A. Paulos

Peepz said...

Thats probably because when people leave the shop they tend to use the left door more often than the right one (which is only used when multiple people exit the same time

Edvin said...

I would expect people to use the right door according to traffic conventions. Might there be a reason why people would be heading left after exiting the store (nearby parking lot, better walkways, etc. ) ?

Robert W. Jernigan said...

Yes, most of the other shops and parking are out the door and to the left!

King Monkey said...

it's likely the lefthand door has a higher distribution because of bags.

as a person goes through the door they turn slightly to face the door.

anyone wearing bags / backpacks naturally turn the bag towards and into the door, thus catching it.