Based on the description of the dot plots, we can analyze the center and variability of both distributions (the Olympic final and the U.S. qualifier) as follows:

1. Center of the Distributions:

• Olympic final distribution: The times range from $10.75$ seconds to $11.01$ seconds, and there is no specific cluster. The center of this distribution can be approximated by finding the median or mean. Since the times are fairly close, the center is likely around $10.88$ seconds.

• U.S. qualifier distribution: The times range from $10.94$ seconds to $11.18$ seconds, with a cluster of times from $11.08$ seconds to $11.17$ seconds. The center of this distribution is likely closer to the center of the cluster, around $11.10$ seconds.

Thus, the center of the Olympic final distribution is lower than the center of the U.S. qualifier distribution, indicating that Olympic finalists ran faster times on average than the U.S. qualifiers.

2. Variability of the Distributions:

• Olympic final distribution: The range is from $10.75$ seconds to $11.01$ seconds, giving a variability of $11.01 - 10.75 = 0.26$ seconds.

• U.S. qualifier distribution: The range is from $10.94$ seconds to $11.18$ seconds, giving a variability of $11.18 - 10.94 = 0.24$ seconds.

Although the ranges of the two distributions are very close, the U.S. qualifier distribution has a cluster, suggesting that it might have less variability overall. In contrast, the Olympic final distribution appears more spread out without clustering, so its variability may feel larger even if the range is comparable.

Thus, the variability in the Olympic final distribution is about the same as (or slightly greater than) the variability in the U.S. qualifier distribution.

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Would you like to explore this further with a detailed analysis, or any particular comparisons? Here are five related questions:

1. How do you calculate the mean for each distribution based on the data given?
2. What other measures of central tendency could be useful in comparing the two distributions?
3. How could the shape of the distributions (e.g., clustering) affect the interpretation of variability?
4. What is the significance of having smaller variability in such competitive races?
5. Could environmental factors play a role in the differences between the two events?

Tip: In statistics, the median is often preferred when dealing with small datasets or when outliers are present, as it gives a better sense of the "middle" without being skewed by extreme values.