Three cars goes from A to B in 2mph, 3mph and 4 mph.
In this case Harmonic mean of speed is 2 10/13 mph and while the arithmetic mean is 3 mph.
How do you logically prove that harmonic mean is more exact in this situation.
Three cars goes from A to B in 2mph, 3mph and 4 mph.
In this case Harmonic mean of speed is 2 10/13 mph and while the arithmetic mean is 3 mph.
How do you logically prove that harmonic mean is more exact in this situation.
Instead of three cars, let's make the problem more intuitive by using one car going from A to B at 2 mph, then B to A at 3 mph, then A to B at 4 mph. We wish to find the average speed.
WLOG, suppose the distance from A to B is 1 mile. Then
, which is the harmonic mean of 2, 3, and 4.