Finding Q1, median, and Q3 from five data points

[karush]

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 $$31-19=12$$?

 

[I like Serena]

Re: box plot

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 $$11$$.