1.6:
Random Error
Indeterminate or random errors arise from several uncontrollable variables in successive measurements.
Since these errors can neither be predicted nor estimated, they are never eliminated. Sometimes it is difficult even to identify the individual error sources. Consider an example of random errors from the electrical noise in an instrument. The fluctuations can go in both positive and negative directions and differ in magnitude.
Due to these random variations, the indeterminate errors are scattered. However, for a large data set, the mathematical laws of probability help to find the most probable results in the mean or median.
On plotting the data with random errors, the values distribute in both directions around the most frequently occurring central value. The frequency of occurrence goes down gradually as the values go higher and lower from the central value. Such a distribution plot is known as the Gaussian curve.
1.6:
Random Error
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.