Chauvenet's criterion is a robust method of outlier detection in a data set. Using this criterion, let's analyze whether the value of 58 in the data set is an anomaly that needs to be excluded.
The data set has ten measurements 46, 48, 44, 38, 45, 47, 58, 44, 45, and 43. The first thing we need to do is calculate the mean and the standard deviation of these measurements.
After calculation, the mean is found to be 45.8, and the standard deviation is 4.81.
Next, we need to calculate the deviations of each measurement from the mean. The deviations are simply the absolute difference between each measurement and the mean. The largest deviation among these measurements is 12.2, which corresponds to the value of 58, as expected.
Then we need to calculate the so-called 'd' value, which is the ratio of the largest deviation to the standard deviation. This is found to be 2.535.
To apply Chauvenet's criterion, we set up a threshold probability 'p', which is often set to 0.05, though this can vary depending on the context. Then, calculate the expected count, which is given by the formula n times 2 times the error function of p divided by the square root of 2, where 'n' is the size of the data set, which in this case is 10.
Following the calculations, the expected count is approximately 0.798. Ideally, if 1 or more measurements were expected to be as far from the mean as the largest deviation by random chance, we would consider the large value not to be an anomaly.
However, in our case, the expected count is less than 1. Consequently, the value of 58 is considered an anomalously large value and according to Chauvenet's criterion, it should be excluded.