In a roller-skating rink, the skaters all move at different speeds. Most skate slightly faster or slower than others, but someti
mes an adventuresome skater accelerates to an "outlying" speed that is much higher than that of everyone else, creating a hazard. As a result, skating rinks often post a sign that says:Any skater moving faster than the average speed of all the skaterswill be asked to leave the rink.It is clear what the sign means, but it is statistically nonsensical. If there are 100 skaters in a rink, all skating at slightly varying speeds, what is the best estimate for how many of them are moving faster than the average speed of all the skaters?
is even if 
, and is odd if 
.
is even, since 
.
is odd, since 
.