Question

Hello, I having trouble with finding the median. So I noticed that the median has two 3’s and I can’t remember how to do it.

Answer 1

The data given in ascending order is,

`1,2,2,3,3,3,3,4,4,4,5,9`

Let solve for Q1,Q2, and Q3.

`\begin{gathered} Q_1=(1)/(4)(N+1)^(th)term \\ where,N=12 \\ Q_1=(1)/(4)(12+1)=(1)/(4)(13)=3.25^(th)term=(2+3)/(2)=2.5 \end{gathered}`
`Q_3=(3)/(4)(N+1)=(3)/(4)(12+1)=9.75^(th)term=4`
`Q_2=Median=(3+3)/(2)=3`

Let us now find the Minimum and Maximum value

`\begin{gathered} Minimum\text{ value=1} \\ Maximum\text{ value=9} \end{gathered}`

The box plot is shown below

Then,

`\begin{gathered} Range=9-1=8 \\ \therefore Range=8 \\ \\ Interquartile\text{ range=}Q_3-Q_1=4-2.5=1.5 \\ \therefore Interquartile\text{ range=1.5} \end{gathered}`