Significant Figures

Scientists are limited by the accuracy of their measuring tools. Say you got a friend to use a tape measure to measure your height and then repeated by asking other friends to do the same. Some example results may be

162.3cm, 162.5cm, 162.5cm and 162.4cm

The more results the more reliable a measurement can be made and the average can quickly be calculated.

162.3 + 162.5 + 162.5 + 162.4 = 162.425 cm
                  4

However, there is no way any human can read a metre rule to this level of accuracy, so the true answer, is 162.4 cm – given to four significant figures.

However, if you round off to fewer significant figures too early in a calculation then errors can be introduced. Emili García-Berthou and Carles Alcaraz of the Department of Environmental Sciences at University of Girona reported that, in 2004, that they found errors, most probably rounding errors, in statistical calculations in just over 11% of the journal articles they sampled. Though errors included transcription and typesetting errors, at least one such error appeared in 38% and 25% of the papers of Nature and the British Medical Journal, respectively, during 2001.

 Averages