Question

using the summary statistics below, which of the following numbers belong in the five number summary? choose all that apply. drive distance histogram quantiles: 100.0% maximum 318.9, 99.5% 318.858, 97.5% 310.0475, 90.0% 300.2, 75.0% quartile 294.125, 50.0% median 288.35, 25.0% quartile 281.85, 10.0% 277.19, 2.5% 270, 0.5% 258.805, 0.0% minimum 258.7. summary statistics: mean 288.59158, std dev 9.3119502, std err mean 0.6551865, upper 95% mean 289.8835, lower 95% mean 287.29966, n 202. options: 300.2, 288.59158, 294.125, 318.858, 318.9, 258.7, 277.19, 9.3119502, 281.85, 288.35

Explanation:

Step1: Recall five - number summary components

The five - number summary of a dataset consists of the minimum, the first quartile ($Q_1$, 25th percentile), the median (50th percentile), the third quartile ($Q_3$, 75th percentile), and the maximum.

Step2: Identify values from the table

• Minimum: From the "Quantiles" table, the minimum (0.0% minimum) is 258.7.
• First quartile ($Q_1$): The 25.0% quartile is 281.85.
• Median: The 50.0% median is 288.35.
• Third quartile ($Q_3$): The 75.0% quartile is 294.125.
• Maximum: The 100.0% maximum is 318.9.

Now we check each option:

• 300.2: Not a part of the five - number summary components.
• 288.59158: This is the mean, not part of the five - number summary.
• 294.125: This is the third quartile ($Q_3$), part of the five - number summary.
• 318.858: Not a part of the five - number summary components.
• 318.9: This is the maximum, part of the five - number summary.
• 258.7: This is the minimum, part of the five - number summary.
• 277.19: Not a part of the five - number summary components.
• 9.3119502: This is the standard deviation, not part of the five - number summary.
• 281.85: This is the first quartile ($Q_1$), part of the five - number summary.
• 288.35: This is the median, part of the five - number summary.

Answer:

294.125, 318.9, 258.7, 281.85, 288.35