MHB Q_1, Median, and Q_3 of A,B,C,D & E

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The discussion centers on calculating the first quartile (Q1), median, and third quartile (Q3) for the data set A=18, B=19, C=23, D=31, and E=36. The values are confirmed as Q1=19, median=23, and Q3=31, leading to a calculated interquartile range of 12. However, Wolfram Alpha (W|A) provides an interquartile range of 11 due to its interpolation method, estimating Q1 as 19.25 and Q3 as 30.25. This discrepancy highlights the difference between standard quartile calculations and those that involve interpolation.
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View attachment 1129
$$A=18$$ (first data in list)
$$B=19 Q_1$$
$$C=23$$ (median of list)
$$D=31 Q_3$$
$$E=36$$ (last data of list)

altho the problem doesn't ask for it, but W|A says the interquartile range is $$11$$ but here
$$Q_3-Q_1$$ is $$31-19=12$$?
 
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Re: box plot

karush said:
View attachment 1129
$$A=18$$ (first data in list)
$$B=19 Q_1$$
$$C=23$$ (median of list)
$$D=31 Q_3$$
$$E=36$$ (last data of list)

altho the problem doesn't ask for it, but W|A says the interquartile range is $$11$$ but here
$$Q_3-Q_1$$ is $$31-19=12$$?

Hi karush!

Your answers are all correct using the regular and simple method to determine the quartiles.
The reason W|A gives something different is because W|A interpolates between the numbers.
The actual first quartile is between 19 and 20. W|A interpolates and makes it $$19\frac 14$$.
Similarly W|A interpolates the third quartile to be $$30\frac 14$$, resulting in an interquartile range of $$11$$.
 
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