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The outliers can be plotted on the box-plot as a dot, a small circle, a star, etc. (see example below). There are other representations in which the whiskers can stand for several other things, such as: One standard deviation above and below the mean of the data set; The 9th percentile and the 91st percentile of the data set
A bagplot, or starburst plot, [1] [2] is a method in robust statistics for visualizing two-or three-dimensional statistical data, analogous to the one-dimensional box plot. Introduced in 1999 by Rousseuw et al., the bagplot allows one to visualize the location, spread, skewness , and outliers of a data set.
In the classical boxplot, the box itself represents the middle 50% of the data. Since the data ordering in the contour boxplot is from the center outwards, the 50% central region is defined by the band delimited by the 50% of deepest, or the most central observations.
A common collection of order statistics used as summary statistics are the five-number summary, sometimes extended to a seven-number summary, and the associated box plot. Entries in an analysis of variance table can also be regarded as summary statistics. [1]: 378
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.
In statistics, the concept of the shape of a probability distribution arises in questions of finding an appropriate distribution to use to model the statistical properties of a population, given a sample from that population.
The standard deviation is commonly used in the determination of what constitutes an outlier and what does not. Standard deviation may be abbreviated SD or std dev, and is most commonly represented in mathematical texts and equations by the lowercase Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the ...
The Cumming plot. A Cumming plot as rendered by the EstimationStats web application. In the top panel, all observed values are shown. The effect sizes, sampling distribution, and 95% confidence intervals are plotted on a separate axes beneath the raw data. For each group, summary measurements (mean ± standard deviation) are drawn as gapped lines.