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The ends of the box represent the 25th and 75th quantiles, also expressed as the 1st and 3rd quartile, respectively.
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The difference between the 1st and 3rd quartiles is called the interquartile range.
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The box has lines that extend from each end, sometimes called whiskers. The whiskers extend from the ends of the box to the outermost data point that falls within the distances computed as follows:
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The bracket outside of the box identifies the shortest half, which is the most dense 50% of the observations (Rousseuw and Leroy 1987).
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Click Box Plot.
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For more details about the Customize Graph window, see Customize Graphical Elements in the Using JMP book.