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'm taking a look at intuitionistic propositional logic (IPL). Basically it exclude Double Negation Elimination (DNE) from the set of axiom schemas replacing it with Ex falso quodlibet: ⊥ → p for any proposition p (including both atomic and composite propositions). In IPL, for instance, the Law of Excluded Middle (LEM) p ∨ ¬p is no longer a theorem. My question: aside from the logic formal perspective, is IPL supposed to model/address some specific "kind of world" ? Thanks.
I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...

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