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[SOLVED] Box plot

karush

Well-known member
Jan 31, 2012
2,725
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 \(\displaystyle 31-19=12\)?
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,780
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 \(\displaystyle 11\).