And the answer is simple: they give you a summarized depiction of the distribution of a sample by provided an schematic graph showing the relative position of the The main question people have is what do boxplots tell you. We conclude that the lower whisker is the minimum, and the top whisker is defined by \(Q_3 + 1.5 \times IQR = 55.25\). But now the maximum is 81, which exceeds \(Q_3 + 1.5 \times IQR = 55.25\). Observe that the minimum is 19, and it is greater than \(Q_1 - 1.5 \times IQR = 17.25\). The interquartile range in this case is \(IQR = Q_3 - Q_1 = 41 - 31.5 = 9.5\). The following table shows the data in ascending order: There are lots of descriptive statistics charts that are very useful but they are algebraically laborious to construct, for which ![]() You all the steps after just clicking the button. You can be better off by using a box and whisker plot calculator such as ours, which will show Otherwise, it is defined by \(Q_3 + 1.5 \times IQR\).Ĭonstructing a box plot can be algebraically involved in done by hand, in the sense that lots of calculations are needed. Similarly, if the maximum of the sample is less than \(Q_3 + 1.5 \times IQR\), then the top whisker is defined by the maximum. Otherwise, it is defined by \(Q_1 - 1.5 \times IQR\). So then, if the minimum of the sample is greater than \(Q_1 - 1.5 \times IQR\), then the lower whisker is defined by the minimum. This is provided that the size of the whisker is smaller than \(1.5 \times IQR\), where \(IQR\) is the interquartile range, and it is defined by \(IQR = Q_3 - Q_1\). Now, for the whiskers there is a rule to follow: the bottom whisker is defined by the minimum of the sample,Īnd the top whisker is defined by the maximum of the sample. The top line of the box is defined by the third quartile (\(Q_3\)). The middle line of the box is defined by the median (\(Q_2\)). ![]() ![]() The bottom line of the box is defined by the first quartile (\(Q_1\)). In the graph above you have an example of a how a boxplot looks like: You have the "box" and the whiskers. When the minimum or maximum are too extreme, the "trim" the whisker and we annotate the existence of an outlier. See key features of the distribution of a sample.Ī box-and-whisker plot provides the median as well as the first and third quartiles in its "box", and the minimum and maximum The Box and Whisker Plot, or also known as Box-plot, is a type of graphical depiction of a sample, that provides easy to
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