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In the image, you're calculating the range, variance, and standard deviation for two sets of teacher salaries: **starting salaries** and **average salaries** for 9 states.

For **starting salaries**, the correct answers provided are:
- **Range:** 8,553
- **Variance:** 12,019,753.3
- **Standard deviation:** 3,467.0

Now, you need to do the same calculations for **average salaries** for 9 states:
- The states and corresponding average salaries (listed in the table) are:
  1. South Dakota: 34,709
  2. Tennessee: 42,537
  3. Texas: 41,744
  4. Utah: 40,027
  5. Vermont: 46,622
  6. Virginia: 43,523
  7. Washington: 49,113
  8. West Virginia: 38,384
  9. Wisconsin: 46,390

### To calculate:
1. **Range:** Highest salary - Lowest salary
2. **Variance:** Use the formula \( \frac{\sum{(x_i - \bar{x})^2}}{N} \) where \( \bar{x} \) is the mean salary and \( N \) is the number of states.
3. **Standard Deviation:** The square root of the variance.

Let me compute these values for you.For the **average salaries** of the 9 states, the calculations are as follows:

- **Range:** 14,404
- **Variance:** 17,910,840.4
- **Standard deviation:** 4,232.1

Would you like further clarification on how these calculations were done or additional details on any part?

Here are 5 related questions for further exploration:
1. How would the variance change if one of the salaries increased significantly?
2. Why is the standard deviation useful in analyzing salary distribution?
3. What would happen to the range if all salaries were closer to the mean?
4. How would you interpret the spread of data when the variance is very high?
5. Could you calculate the median salary for both starting and average salaries?

**Tip:** Understanding the variance helps identify how spread out the data points are relative to the mean.

Find the range, variance, and standard deviation of starting and average salaries for 9 states. Round your answers to at least one decimal place.

Learn how to calculate the range, variance, and standard deviation for starting and average teacher salaries across 9 states. This problem focuses on key statistical concepts used in data analysis, including variance and standard deviation, and is suitable for students in Grades 10-12.

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