Questions: Find the 5 number summary for the data shown x 10.7 11.1 21.9 22.5 24.1 5 number summary: Use the Locator/Percentile method described in your book, not your calculator.

Find the 5 number summary for the data shown

x
10.7
11.1
21.9
22.5
24.1

5 number summary:

Use the Locator/Percentile method described in your book, not your calculator.

Transcript text: Find the 5 number summary for the data shown \begin{tabular}{|c|} \hline $\mathbf{x}$ \\ \hline 10.7 \\ \hline 11.1 \\ \hline 21.9 \\ \hline 22.5 \\ \hline 24.1 \\ \hline \end{tabular} 5 number summary: $\square$ $\square$ $\square$ $\square$ $\square$ Use the Locator/Percentile method described in your book, not your calculator.

Solution

Solution Steps

Step 1: Minimum Value

The minimum value of the dataset is given by the smallest observation: \[ \text{Minimum} = 10.7 \]

Step 2: First Quartile (Q1)

To find the first quartile $ Q_1 $, we use the formula for the rank: \[ \text{Rank} = Q \times (N + 1) = 0.25 \times (5 + 1) = 1.5 \] Since the rank is not an integer, we take the average of the values at positions 1 and 2: \[ Q_1 = \frac{X_{\text{lower}} + X_{\text{upper}}}{2} = \frac{10.7 + 11.1}{2} = 10.9 \]

Step 3: Median (Q2)

The median $ Q_2 $ is found using the rank: \[ \text{Rank} = Q \times (N + 1) = 0.5 \times (5 + 1) = 3.0 \] Since the rank is an integer, the median corresponds to the value at position 3: \[ Q_2 = 21.9 \]

Step 4: Third Quartile (Q3)

To find the third quartile $ Q_3 $, we calculate the rank: \[ \text{Rank} = Q \times (N + 1) = 0.75 \times (5 + 1) = 4.5 \] Since the rank is not an integer, we take the average of the values at positions 4 and 5: \[ Q_3 = \frac{X_{\text{lower}} + X_{\text{upper}}}{2} = \frac{22.5 + 24.1}{2} = 23.3 \]

Step 5: Maximum Value

The maximum value of the dataset is given by the largest observation: \[ \text{Maximum} = 24.1 \]