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In statistics, an outlier is a data point that differs significantly from other observations. [ 1 ] [ 2 ] An outlier may be due to a variability in the measurement, an indication of novel data, or it may be the result of experimental error; the latter are sometimes excluded from the data set .
Because the whiskers must end at an observed data point, the whisker lengths can look unequal, even though 1.5 IQR is the same for both sides. All other observed data points outside the boundary of the whiskers are plotted as outliers. [10] The outliers can be plotted on the box-plot as a dot, a small circle, a star, etc. (see example below).
In statistics, Grubbs's test or the Grubbs test (named after Frank E. Grubbs, who published the test in 1950 [1]), also known as the maximum normalized residual test or extreme studentized deviate test, is a test used to detect outliers in a univariate data set assumed to come from a normally distributed population.
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, at 95% confidence, Q = 0.455 < 0.466 = Q table 0.167 is not considered an outlier. McBane [1] notes: Dixon provided related tests intended to search for more than one outlier, but they are much less frequently used than the r 10 or Q version that is intended to eliminate a single outlier.
Deviations from a straight line suggest departures from normality. The plotting can be manually performed by using a special graph paper, called normal probability paper. With modern computers normal plots are commonly made with software. The normal probability plot is a special case of the Q–Q probability plot for a normal distribution.
The outliers would greatly change the estimate of location if the arithmetic average were to be used as a summary statistic of location. The problem is that the arithmetic mean is very sensitive to the inclusion of any outliers; in statistical terminology, the arithmetic mean is not robust.
The usual estimate of σ 2 is the internally studentized residual ^ = = ^. where m is the number of parameters in the model (2 in our example).. But if the i th case is suspected of being improbably large, then it would also not be normally distributed.