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In this chart, outliers are defined as mild above Q3 + 1.5 IQR and extreme above Q3 + 3 IQR. The interquartile range is often used to find outliers in data. Outliers here are defined as observations that fall below Q1 − 1.5 IQR or above Q3 + 1.5 IQR.
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).
Outliers can be detected in a functional boxplot by the 1.5 times the 50% central region empirical rule, analogous to the 1.5 IQR empirical rule for classical boxplots. The fences are obtained by inflating the envelope of the 50% central region by 1.5 times the height of the 50% central region.
Interquartile range (IQR) is defined as the difference between the 75th and 25th percentiles or Q 3 - Q 1. While the maximum and minimum also show the spread of the data, the upper and lower quartiles can provide more detailed information on the location of specific data points, the presence of outliers in the data, and the difference in spread ...
The modified Thompson Tau test is used to find one outlier at a time (largest value of δ is removed if it is an outlier). Meaning, if a data point is found to be an outlier, it is removed from the data set and the test is applied again with a new average and rejection region. This process is continued until no outliers remain in a data set.
The sample maximum and minimum are the least robust statistics: they are maximally sensitive to outliers.. This can either be an advantage or a drawback: if extreme values are real (not measurement errors), and of real consequence, as in applications of extreme value theory such as building dikes or financial loss, then outliers (as reflected in sample extrema) are important.
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Since it is based on quantile information, it is less sensitive to outliers than measures such as the coefficient of variation. As such, it is one of several robust measures of scale. The statistic is easily computed using the first and third quartiles, Q 1 and Q 3, respectively) for each data set.