Questions: Find the 5 number summary for the data shown x 5 9 11.3 14.9 15.3 17.9 25 29.4 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 5 9 11.3 14.9 15.3 17.9 25 29.4 5 number summary: Use the Locator/Percentile method described in your book, not your calculator.

Solution

Solution Steps

Step 1: Data Overview

The given dataset consists of the following values: \[ x = \{5, 9, 11.3, 14.9, 15.3, 17.9, 25, 29.4\} \]

Step 2: Calculate Minimum and Maximum

The minimum value in the dataset is: \[ \text{Minimum} = 5 \] The maximum value in the dataset is: \[ \text{Maximum} = 29.4 \]

Step 3: Calculate First Quartile (Q1)

The first quartile \( Q_1 \) is calculated as: \[ Q_1 \approx 10.73 \]

Step 4: Calculate Median

The median \( Q_2 \) is calculated as: \[ Q_2 \approx 15.1 \]

Step 5: Calculate Third Quartile (Q3)

The third quartile \( Q_3 \) is calculated as: \[ Q_3 \approx 19.67 \]

Final Answer

The 5-number summary is: \[ \text{Minimum} = 5, \quad Q_1 \approx 10.73, \quad \text{Median} \approx 15.1, \quad Q_3 \approx 19.67, \quad \text{Maximum} = 29.4 \] Thus, the final answer is: \[ \boxed{\{5, 10.73, 15.1, 19.67, 29.4\}} \]

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