Using mobile-device sensors to teach students error analysis

Science students must deal with the errors inherent to all physical measurements and be conscious of the need to expressvthem as a best estimate and a range of uncertainty. Errors are routinely classified as statistical or systematic. Although statistical errors are usually dealt with in the first years of science studies, the typical approaches are based on manually performing repetitive observations. Our work proposes a set of laboratory experiments to teach error and uncertainties based on data recorded with the sensors available in many mobile devices. The main aspects addressed are the physical meaning of the mean value and standard deviation, and the interpretation of histograms and distributions. The normality of the fluctuations is analyzed qualitatively comparing histograms with normal curves and quantitatively comparing the number of observations in intervals to the number expected according to a normal distribution and also performing a Chi-squared test. We show that the distribution usually follows a normal distribution, however, when the sensor is placed on top of a loudspeaker playing a pure tone significant differences with a normal distribution are observed. As applications to every day situations we discuss the intensity of the fluctuations in different situations, such as placing the device on a table or holding it with the hands in different ways. Other activities are focused on the smoothness of a road quantified in terms of the fluctuations registered by the accelerometer. The present proposal contributes to gaining a deep insight into modern technologies and statistical errors and, finally, motivating and encouraging engineering and science students.