Uncertainty
Analyze measurement uncertainties
Autor:
Título 4
Learning objectives :
This activity helps students understand the difference between signal and noise in a physical measurement. It develops critical thinking when faced with data and the statistical approach in experimental sciences.
Concepts covered
Statistical distribution of measurements; Signal-to-noise ratio; Standard deviation and variance; MEMS gyroscope; Accuracy vs Precision
What students will do :
The student compares the data from the FizziQ gyroscope in two situations: smartphone stationary then rotating. By analyzing the histograms of the two measurements, the student observes the difference in distribution and standard deviation and deduces how to differentiate a real signal from the background noise inherent to any measuring instrument.
What is required :
Smartphone with the FizziQ application; Clear space to turn safely; Optional: turntable for additional comparison; FizziQ experience notebook
Scientific background :
A smartphone's gyroscope is a MEMS (Micro Electro Mechanical Systems) sensor that measures the rotation speed around the three axes. Even when the device is perfectly still, the sensor records small, random fluctuations around zero, consisting mainly of electronic noise and environmental micro-vibrations. These fluctuations generally follow a normal (Gaussian) distribution centered on zero, characterized by its standard deviation σ. This standard deviation defines the limit sensitivity of the sensor: any signal whose amplitude is less than 2-3σ risks being indistinguishable from the noise. When the smartphone is rotated, a real signal is added to the background noise. The histogram then changes considerably: the distribution widens, shifts, and can even become bimodal or multimodal depending on the type of movement. The standard deviation increases significantly, reflecting the wider dispersion of the measured values. In metrology, there are two fundamental concepts: precision (reproducibility of measurements, linked to the standard deviation) and accuracy (proximity to the real value). A sensor can be precise but inaccurate if its measurements are consistent with each other but offset from reality (systematic bias). The experiment with a turntable allows us to deepen the analysis by comparing a regular movement (constant rotation) to a naturally more variable human movement. Modern smartphone gyroscopes achieve a precision of around ±0.1-0.5°/s, sufficient for many applications such as games or augmented reality.