Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be approximately characterized by enumerating the frequencies of observations in a large dataset. Characterizing the collective effect of these errors helps with statistical analyses. Take a large data set of temperature measurements in London, for instance. We can plot the magnitude of temperature vs. the frequency of occurrence, and if the variations (or errors) in the temperature are truly random, we will obtain a normal distribution curve, also known as the Gaussian curve. This curve allows us to apply the mathematical laws of probability to estimate the mean value and the deviation from the mean value, also known as the standard deviation. From there, we can perform tests to eliminate outliers and answer questions about the dataset.

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