Open AccessIn teaching mathematical statistics it is desirable that students of engineering and natural sciences could study the methods of statistical processing based on data of real experiments. Conditions for these experiments are of critical importance to justify the application of statistical methods.
The article considers a classic Henry Cavendish’s experiment to determine a mean density of the Earth from this point of view. The article gives a detailed description of the experimental Cavendish’s setup, ideas, his experiments are based on, and a method to determine the values used for assessment of the mean density of the Earth. It also concretizes the equation of a pendulum model with friction on which Cavendish implicitly (and neglecting a friction) relied.
It is shown that the formal use of methods of mathematical statistics is not always justified. Detailed records of all experiments, published by Cavendish, enable us to study these data in terms of mathematical statistics, convince us of their statistical inhomogeneity and impossibility to construct a confidence interval to estimate accuracy.
The article proposes an alternative way for processing Cavendish's data implicitly using the pendulum model equation with friction to reduce an effect of systematic errors and improve matching the Cavendish results with modern data.