On measuring average speed in a circulating system

Abstract

The paper considers measuring speeds of vehicles which move in a circular track. By using the Schwarz inequality, it is shown that the average speed of the vehicles is over-estimated when the vehicles are observed at a fixed point in the track. It is also illustrated that the relative error is the square of an important statistical quantity, the coefficient of variation of the distribution of vehicle speeds. The results are interesting and the techniques used are elementary mathematics and statistics.