To determine the best way to measure the spread of the data, it's important to consider the presence of outliers. The Interquartile Range (IQR) is typically more resistant to outliers, while the standard deviation can be heavily influenced by them.

Let’s analyze the data for both college and high school students:

College:

• Max: 50
• Min: 6
• IQR: 17 - 8.5 = 8.5
• Mean: 15.4
• σ (standard deviation): 11.7

The difference between the max and min values for college students is quite large, indicating the potential for outliers. Since the IQR is more robust against outliers, the college spread is better described by the IQR.

High School:

• Max: 28
• Min: 3
• IQR: 15 - 4.5 = 10.5
• Mean: 10.5
• σ (standard deviation): 5.8

For high school students, the spread is more compact, and there is less indication of significant outliers. Hence, the standard deviation may be a better measure here.

Conclusion:

The college spread is best described by the IQR, and the high school spread is best described by the standard deviation.

So, the correct answer is:

• The college spread is best described by the IQR. The high school spread is best described by the standard deviation.

Would you like more details or have any questions about this?

Here are 5 related questions to consider:

1. What is the impact of outliers on the standard deviation?
2. How can you identify outliers using IQR?
3. Why is the IQR a better measure of spread in skewed distributions?
4. How is the standard deviation calculated?
5. In which cases would the range be a better measure of spread than both the IQR and standard deviation?

Tip: When checking for outliers, remember that values beyond 1.5 times the IQR from the quartiles are typically considered outliers.