I Box & Whisker Plot: When, How & Difference

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Box and whisker plots are useful for visualizing data distribution and identifying outliers, making them ideal for data exploration. They are particularly effective when dealing with heteroskedastic data, as they can highlight variations in data spread. The main difference between box plots and other statistical methods lies in their ability to summarize data through quartiles and visualize the median, which is not always evident in other graphical representations. While not commonly used in published work, they provide valuable insights during preliminary data analysis. Overall, box and whisker plots serve as a powerful tool for understanding data characteristics.
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the usage of box and whisker plot
I know the steps of box and whisker plot, but when should I use it? how can I classify its problems?, what is the difference between it and other statistical methods?
 
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I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...

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