Using the data: 2, 2, 3, 3, 3, 4, 5, 6, 6, 19What is Q1 and Q3 3.5, 6.5 2, 10 3, 6 2, 5

Accepted Solution

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 formulasFor 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]