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

[karush]

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

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

 

[I like Serena]

Re: box plot

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

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

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 \(\displaystyle 19\frac 14\).
Similarly W|A interpolates the third quartile to be \(\displaystyle 30\frac 14\), resulting in an interquartile range of \(\displaystyle 11\).