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First, the statistician may remove the suspected outliers from the data set and then use the arithmetic mean to estimate the location parameter. Second, the statistician may use a robust statistic, such as the median statistic. Peirce's criterion is a statistical procedure for eliminating outliers.
The idea behind Chauvenet's criterion finds a probability band that reasonably contains all n samples of a data set, centred on the mean of a normal distribution.By doing this, any data point from the n samples that lies outside this probability band can be considered an outlier, removed from the data set, and a new mean and standard deviation based on the remaining values and new sample size ...
However, multiple iterations change the probabilities of detection, and the test should not be used for sample sizes of six or fewer since it frequently tags most of the points as outliers. [3] Grubbs's test is defined for the following hypotheses: H 0: There are no outliers in the data set H a: There is exactly one outlier in the data set
To apply a Q test for bad data, arrange the data in order of increasing values and calculate Q as defined: Q = gap range {\displaystyle Q={\frac {\text{gap}}{\text{range}}}} Where gap is the absolute difference between the outlier in question and the closest number to it.
Naive interpretation of statistics derived from data sets that include outliers may be misleading. For example, if one is calculating the average temperature of 10 objects in a room, and nine of them are between 20 and 25 degrees Celsius, but an oven is at 175 °C, the median of the data will be between 20 and 25 °C but the mean temperature ...
A typical strategy to account for, without eliminating altogether, these outlier values is to 'reset' outliers to a specified percentile (or an upper and lower percentile) of the data. For example, a 90% winsorization would see all data below the 5th percentile set to the 5th percentile, and all data above the 95th percentile set to the 95th ...
A simple example is fitting a line in two dimensions to a set of observations. Assuming that this set contains both inliers, i.e., points which approximately can be fitted to a line, and outliers, points which cannot be fitted to this line, a simple least squares method for line fitting will generally produce a line with a bad fit to the data including inliers and outliers.
The four datasets composing Anscombe's quartet. All four sets have identical statistical parameters, but the graphs show them to be considerably different. Anscombe's quartet comprises four datasets that have nearly identical simple descriptive statistics, yet have very different distributions and appear very different when graphed.
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