Does averaging two readings reduce the error? Imagine you have a therometer measuring the temperature over time, resulting in a series of readings: [90, 95, 100…] There could be two reasons for the variation in these numbers: the actual temperature is changing, or the thermometer is inaccurate and showing changing numbers for a constant temperature. For the purpose of this problem, you can assume that that the temperature is constant, so a perfect thermometer would return [100, 100, 100, 100, 100, 100, 100…] But we don’t have a perfect thermometer, resulting in error in the measurement. The error is determined by the standard deviation. We want to reduce the error. Someone suggests installing two thermometers: thermometer1 = [90, 95, 100…] thermometer2 = [92, 97, 94…] Then you take the average of the ith values of each thermometer: average = [91, 96, 97…] The question is whether the average has lower error than just using one thermometer. Build a simulation to test thousands of different scenarios and answer the question empirically.
