To solve this problem, let's first analyze the data presented in the table.

Data Summary:

• The table provides statistics about the amount of time students from either college or high school spend on homework each week.
• Data includes High, Low, Q1 (first quartile), Q3 (third quartile), IQR (interquartile range), Median, Mean, and σ (standard deviation).

College:

• High: 20 hours
• Low: 6 hours
• Q1: 8 hours
• Q3: 18 hours
• IQR: 10 hours
• Median: 14 hours
• Mean: 13.3 hours
• Standard Deviation (σ): 5.2 hours

High School:

• High: 20 hours
• Low: 3 hours
• Q1: 5.5 hours
• Q3: 16 hours
• IQR: 10.5 hours
• Median: 11 hours
• Mean: 11 hours
• Standard Deviation (σ): 5.4 hours

Spread of Data:

To choose the correct option for describing the spread of the data, let's break down each choice:

1. IQR (Interquartile Range): Measures the spread of the middle 50% of data (from Q1 to Q3). It’s less affected by outliers and skewed data.

2. Standard Deviation (σ): Measures the average amount of variability in the data, accounting for all data points. It is more sensitive to outliers and extremes.

Options Analysis:

• Option 1: "Both spreads are best described by the IQR."

  • IQR is useful when data may have outliers or is skewed. However, both data sets have a standard deviation provided, which usually means variability across the whole data set is important. So this option may not be the best.

• Option 2: "Both spreads are best described by the standard deviation."

  • Since both college and high school have similar standard deviations (5.2 and 5.4), and standard deviation considers the entire range of data (including potential outliers), this seems like a strong option.

• Option 3: "The college spread is best described by the IQR. The high school spread is best described by the standard deviation."

  • The IQR for both groups is quite similar (10 and 10.5), and this doesn't suggest that one group's data should be more influenced by the IQR than the other.

• Option 4: "The college spread is best described by the standard deviation. The high school spread is best described by the IQR."

  • There's no clear reason to describe high school data by the IQR while using standard deviation for college data, especially since their spreads are similar in both metrics.

Conclusion:

The best answer appears to be Option 2: Both spreads are best described by the standard deviation, as standard deviation provides a more complete picture of the spread by accounting for all data points, including outliers.

Would you like any further details or have more questions?

Here are five related questions for further practice:

1. What is the significance of the IQR when analyzing data with outliers?
2. How does skewness in data affect the use of the mean and standard deviation?
3. When should you prefer median and IQR over mean and standard deviation for describing data?
4. What is the relationship between range and standard deviation?
5. How does the standard deviation change when all data