# [SOLVED]Box plot

#### karush

##### Well-known member
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
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 $$\displaystyle 11$$.