Questions: Find the first and third quartile for the quantitative data. x 3.7 6 8.6 13.5 16.1 19 20.1 23.2 23.9 24.4 Q1= Q3=

Transcript text: Find the first and third quartile for the quantitative data. \begin{tabular}{|r|} \hline \multicolumn{1}{|c|}{$x$} \\ \hline 3.7 \\ \hline 6 \\ \hline 8.6 \\ \hline 13.5 \\ \hline 16.1 \\ \hline 19 \\ \hline 20.1 \\ \hline 23.2 \\ \hline 23.9 \\ \hline 24.4 \\ \hline \end{tabular} \[ \begin{array}{l} Q_{1}= \\ Q_{3}= \end{array} \]

Solution

Solution Steps

Step 1: Sort the Data

The sorted data set is: [3.7, 6, 8.6, 13.5, 16.1, 19, 20.1, 23.2, 23.9, 24.4].

Step 2: Calculate Positions for Q1 and Q3

The position for Q1 (P_Q1) is calculated as $\frac14 \times (10 + 1) = 2.75$. The position for Q3 (P_Q3) is calculated as $\frac34 \times (10 + 1) = 8.25$.

Step 3: Determine Quartiles

Since P_Q1 is not an integer, Q1 is interpolated between positions 2 and 3, resulting in 7.3. Since P_Q3 is not an integer, Q3 is interpolated between positions 8 and 9, resulting in 23.55.