Let 'y' be the no. of library books checked out per month, and 'x' be the corresponding frequency.
Then, from the dot plot the data is obtained as,
[tex]0,2,2,3,4,4,7,8,8,10,10,11,16[/tex]There are 13 no. of data points i.e. even, so the median i.e. second quartile will be calculater as,
[tex]\begin{gathered} \text{Median}=(\frac{13+1}{2})th\text{ term} \\ Q_2=(7)th\text{ term} \\ Q_2=7 \end{gathered}[/tex]Then the first quartile will be the median of the data before the second quartile,
[tex]\begin{gathered} Q_1=Avg\mleft\lbrace(\frac{6}{2})th\text{ term and }(\frac{6}{2}+1)th\text{ term}\mright\rbrace \\ Q_1=Avg\lbrace(3)rd\text{ term and }(4)th\text{ term}\rbrace \\ Q_1=Avg\lbrace2\text{ and }3\rbrace \\ Q_1=\frac{2+3}{2} \\ Q_1=2.5 \end{gathered}[/tex]Similarly the third quartile will be the median of the last 6 data points,
[tex]\begin{gathered} Q_3=Avg\mleft\lbrace(\frac{6}{2})th\text{ }term\text{ }after\text{ }Q_2\text{ }and\text{ }(\frac{6}{2}+1)th\text{ }term\text{ }after\text{ }Q_2\mright\rbrace \\ Q_3=Avg\lbrace(3)rd\text{ }term\text{ }after\text{ }Q_2\text{ }and\text{ }(4)th\text{ }term\text{ }after\text{ }Q_2\rbrace \\ Q_3=Avg\lbrace10\text{ }and\text{ }10\rbrace \\ Q_3=10 \end{gathered}[/tex]Observe that only the second option satisfied all three given conditions, so this will be the correct choice.