There is a constant search for a more accurate measurement, which generally leads to higher cost, greater complexity, or devices that do not lend themselves to manufacturing environments. We present a method of using statistical sampling to improve metrological accuracy without these undesirable effects. For metrology of flat surfaces and steps between flat surfaces, this method demonstrated precision improvement up to a factor of 55, and accuracy increase of at least a factor of 10. The corresponding precision and accuracy improvements on a spherical surface were both factors of 8. Since this accuracy improvement can be implemented in software, it does not affect the speed of measurement or the complexity of the hardware, and it can be used to improve the accuracy of a wide range of metrology systems.