Answer: Third Option
[tex]Q_1=3[/tex]
[tex]Q_3=6[/tex]
Step-by-step explanation:
Notice that we already have the data sorted from least to greatest.
Now to find Q1 and Q3 we can use the following formulas
For a set of data ordered from least to greatest of the form [tex]X_1, X_2, ..., X_n[/tex]
Where n is the total number of data
[tex]Q_1=X_{\frac{1}{4}(n+1)}[/tex]
In this case [tex]n=10[/tex]
So:
[tex]Q_1=X_{\frac{1}{4}(10+1)}[/tex]
[tex]Q_1=X_{2.75}[/tex]
Round the nearest whole and get:
[tex]Q_1=X_{3}[/tex]
[tex]Q_1=3[/tex]
For [tex]Q_3[/tex] we have:
[tex]Q_3=X_{\frac{3}{4}(n+1)}[/tex]
[tex]Q_3=X_{\frac{3}{4}(10+1)}[/tex]
[tex]Q_3=X_{8.25}[/tex]
Round the nearest whole and get:
[tex]Q_3=X_{8}[/tex]
[tex]Q_3=6[/tex]
