A home-lab to study uncertainties using smartphone sensors and determine the optimal number of measurements

TL;DR

This paper describes a home-lab activity using smartphone sensors to teach students about measurement uncertainties, error analysis, and optimal measurement strategies, leveraging accessible technology for educational purposes.

Contribution

It introduces a practical, smartphone-based experimental approach for teaching error analysis and uncertainty concepts in science education, especially during remote learning.

Findings

Smartphone sensors can effectively teach error analysis.

Optimal number of measurements depends on sensor resolution and standard error.

Experimental fluctuations can be analyzed using Gaussian distribution.

Abstract

We present a home-lab experimental activity, successfully proposed to our students during covid19 pandemic, based on \textit{state-of-the-art} technologies to teach error analysis and uncertainties to science and engineering students. In the last decade the appearance of smartphones considerably affected our daily life. Thanks to their built-in sensors, this revolution has impacted in many areas and, in particular, the educational field. Here we show how to use smartphone sensors to teach fundamental concepts for science students such as any measurement is useless unless a confidence interval is specified or how to determine if a result agrees with a model, or to discern a new phenomenon from others already known. We explain how to obtain and analyse experimental fluctuations and discuss in relation with the Gaussian distribution. In another application we show how to determine the optimal number of measurements as a function of the standard error and the digital resolution of a given sensor.