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Figure 2. Box-plot with whiskers from minimum to maximum Figure 3. Same box-plot with whiskers drawn within the 1.5 IQR value. A boxplot is a standardized way of displaying the dataset based on the five-number summary: the minimum, the maximum, the sample median, and the first and third quartiles.
Box-and-whisker plot with four mild outliers and one extreme outlier. 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.
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.
The five-number summary is a set of descriptive statistics that provides information about a dataset. It consists of the five most important sample percentiles: the sample minimum (smallest observation) the lower quartile or first quartile; the median (the middle value) the upper quartile or third quartile
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.
Box plot of the Michelson–Morley experiment, showing several summary statistics. In descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate the largest amount of information as simply as possible. Statisticians commonly try to describe the observations in
Whereas statistics and data analysis procedures generally yield their output in numeric or tabular form, graphical techniques allow such results to be displayed in some sort of pictorial form. They include plots such as scatter plots , histograms , probability plots , spaghetti plots , residual plots, box plots , block plots and biplots .
The observation in the box indicates the median, or the most central observation which is also a robust statistic to measure centrality. The "whiskers" of the boxplot are the vertical lines of the plot extending from the box and indicating the maximum envelope of the dataset except the outliers.