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In the given task, you are asked to assign appropriate measures of center and spread for the dot plots of the Junior Varsity and Varsity teams. The characteristics of the distributions shown in the dot plots will help determine which statistics to use.

### Analysis of the Dot Plots

#### Junior Varsity Team
- **Distribution Shape**: The data points appear fairly symmetrically distributed around a central value with no outliers.
- **Appropriate Measures**:
  - **Measure of Center**: The mean or median would be appropriate here due to the symmetry. However, the median is typically preferred as it is less sensitive to slight asymmetries and potential outliers not visible in the plot.
  - **Measure of Spread**: Standard deviation could be used because the distribution does not have visible outliers and is fairly symmetric.

#### Varsity Team
- **Distribution Shape**: The distribution appears slightly skewed with a potential outlier on the higher end.
- **Appropriate Measures**:
  - **Measure of Center**: The median is preferred over the mean as the data shows skewness which can affect the mean more significantly.
  - **Measure of Spread**: The interquartile range (IQR) is ideal here since it is resistant to the influence of outliers and skewness.

### Conclusion

Here’s how you should assign the measures:

- **Junior Varsity Team**:
  - **Measure of Center**: Median
  - **Measure of Spread**: Standard Deviation

- **Varsity Team**:
  - **Measure of Center**: Median
  - **Measure of Spread**: Interquartile Range

Do you have any other questions or need further details on this topic? Here are some follow-up questions you might consider:

1. What is the difference between mean and median, and why does skewness affect them differently?
2. How do you calculate the standard deviation and interquartile range?
3. Why is the median less sensitive to outliers compared to the mean?
4. Can the mean still be used effectively for the Varsity team? Why or why not?
5. What are some other statistics that can be used to describe skewed distributions?

**Tip**: Always check for the presence of outliers and the symmetry of the distribution when choosing the appropriate measures of center and spread to get the most accurate description of the data.

A cross country coach records the number of miles his athletes on the Junior Varsity and Varsity teams ran today and displays the data in dot plots. Given the shape of each distribution, determine which measures of center and spread are appropriate for him to use to summarize the data from each team.

Learn how to determine the appropriate measures of center and spread for the Junior Varsity and Varsity teams' data distributions. This example illustrates when to use the median, mean, standard deviation, and interquartile range based on data symmetry and skewness. Suitable for high school students.

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