
Before sending track and field athletes to the Olympics, the U.S. holds a qualifying meet.
The lower dot plot shows the times (in seconds) of the 
\[8\] sprinters who competed in the final of the women's 
\[100\]-meter dash at the 
\[2012\] Olympic games. The upper dot plot shows the times (in seconds) of the top 
\[8\] sprinters at the U.S. qualifying meet for that event.
A double dot plot with the upper half modeling the U S qualifier and the lower half models the Olympic final. The number line is labeled time in seconds. The U S Qualifier dots range from 10 and 94 hundredths to 11 and 18 hundredths. There is a cluster of the dots ranging from 11 and 8 hundredths to 11 and 17 hundredths. The Olympic final dots have no cluster and range from 10 and 75 hundredths to 11 and 1 hundredth.
\[10.7\]
\[10.8\]
\[10.9\]
\[11\]
\[11.1\]
\[11.2\]
The center of the Olympic final distribution is 

 the center of the US qualifier distribution.
The variability in the Olympic final distribution is 

 the variability in the US qualifier distribution.


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.

---

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.

Before sending track and field athletes to the Olympics, the U.S. holds a qualifying meet. The lower dot plot shows the times (in seconds) of the [8] sprinters who competed in the final of the women's [100]-meter dash at the [2012] Olympic games. The upper dot plot shows the times (in seconds) of the top [8] sprinters at the U.S. qualifying meet for that event. A double dot plot with the upper half modeling the U.S. qualifier and the lower half models the Olympic final. The number line is labeled time in seconds. The U.S. Qualifier dots range from 10.94 seconds to 11.18 seconds. There is a cluster of the dots ranging from 11.08 seconds to 11.17 seconds. The Olympic final dots have no cluster and range from 10.75 seconds to 11.01 seconds. What is the center of the Olympic final distribution compared to the U.S. qualifier distribution? How does the variability in the Olympic final distribution compare to the U.S. qualifier distribution?

Explore how to analyze dot plots by comparing the U.S. qualifier and Olympic final times of the top sprinters in the women's 100-meter dash at the 2012 Olympics. Learn about the center of the distributions, variability, and how to calculate measures like the mean and range. This is a great resource for high school students in Grades 10-12.

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