A star cluster is a collection of gravitationally bound star

A star cluster is a collection of gravitationally bound stars. Individual stars in the cluster move about with different velocities but the average of all these should give the velocity of the cluster as a whole. An astronomer measures the radial velocities of four stars in a cluster that contains 1000 stars. They are 74, 41, 61, and 57 km/s .How any additional stars should he measure if he wishes to achieve a precision of 2 km/s for the radial velocity of the cluster as a whole?

Solution

74+41+61+57 =233/4 = 58.25

58.25 +/- 2/1000

58.25 +/- 0.002