I may need to correct part of my earlier message. Minitab computes quartiles as I said. I thought the versions I've used in the past used these to construct a boxplot but documentation for recent editions says they use Tukey hinges.
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I am not familiar with this particular version of Minitab, but traditionally Minitab has used the 1.5XIQR rule for detecting outliers. However, it computes the IQR by subtracting the first quartile from the third. Despite what they say, this is not what Moore and McCabe do. Use "describe" on your data and see if you and Minitab agree on Q1 and Q3.
Minitab approaches quartiles using a general approach that fits all kinds of quantiles -- deciles, percentiles, etc. In this system, Q1 has rank 0.25(n+1) and Q3 has rank 0.75(n+1). You can see that this could involve interpolating one-fourth or three-fourths of the way between adjacent data values, while this could never happen with the procedure used in Moore and McCabe.
When Tukey invented the boxplot he used approximate quartiles which he called "hinges". He wanted simple techniques that could be implemented quickly without any computing machinery. Minitab could use these hinges and get boxplots exactly like Tukey's, or it could take the position that hinges are only approximations to quartiles, and so quartiles are the thing to use and Tukey's handmade boxplots are only approximations to the "correct" ones Minitab produces. They seem to have taken the latter position.
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