16. Lised below are the numbers ot hurricanes that occurred in each year in a certan region. The data are isted in order by year, Find the range, variance, and standard devation for the given sample data. include appropits in the resuls. What important feature of the data is not revealed by any of the measures of vailation? The rarge of the sample data is \( \square \) (Round to one decimal place as needed.)

1. **Determine the Range**   The range is defined as the difference between the largest and smallest values in the sample. If we denote the smallest value by \( x_{\min} \) and the largest value by \( x_{\max} \), then \[ \text{Range} = x_{\max} - x_{\min}. \]   After identifying the minimum and maximum values from the given list, you subtract to obtain the range. (Remember to round your final answer to one decimal place if needed.) For example, if the smallest hurricane count were 0 and the largest were 9, then \[ \text{Range} = 9 - 0 = 9.0. \] 2. **Compute the Sample Variance**   First, calculate the sample mean: \[ \bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i, \]   where \( n \) is the number of years (data points) in the sample and \( x_i \) represents the hurricane count in year \( i \).   Then, the sample variance is given by \[ s^2 = \frac{1}{n-1}\sum_{i=1}^{n} (x_i - \bar{x})^2. \]   You first subtract the mean from each data value, square the result, sum all the squared differences, and finally divide by \( n-1 \). (Round the result to an appropriate number of decimal places.) 3. **Compute the Sample Standard Deviation**   The standard deviation is the square root of the variance: \[ s = \sqrt{s^2}. \]   Again, round the final answer to one decimal place as necessary. 4. **Identify an Important Feature Not Revealed by These Measures**   Although the range, variance, and standard deviation describe aspects of how spread out the data values are, none of these measures reveal the overall shape of the distribution. In particular, they do not inform you if the data are symmetric, skewed, or if there is more than one cluster (bimodality) in the data. This feature, the distribution shape, is critical for understanding the nature of the data beyond its spread. 5. **Final Answers Format**   - The range of the sample data is: \( x_{\max} - x_{\min} \) (for example, \( 9.0 \), if \( x_{\max}=9 \) and \( x_{\min}=0 \)).   - The sample variance is: \[ s^2 = \frac{1}{n-1}\sum_{i=1}^{n} (x_i - \bar{x})^2. \]   - The sample standard deviation is: \[ s = \sqrt{\frac{1}{n-1}\sum_{i=1}^{n} (x_i-\bar{x})^2}. \]   - The important feature not revealed by these measures is the overall shape of the distribution (for example, whether the data are symmetric, skewed, or bimodal). Replace \( x_{\min} \), \( x_{\max} \), \( n \), and the values \( x_i \) with the corresponding numbers from your list of hurricane counts to obtain numerical answers.