Listed below are prices in dollars for one night at different hotels in a certain region. Find the range, variance, and standard deviation for the given sample data. Include appropriate units in the results. How useful are the measures of variation for someone searching for a room? 197 187 160 98 202 109 228 121

Step 1 ：Given the hotel prices are: 197, 187, 160, 98, 202, 109, 228, 121 dollars for one night.

Step 2 ：The range is calculated as the difference between the highest and lowest values. In this case, the range is \(228 - 98 = 130\) dollars.

Step 3 ：The variance is calculated as the average of the squared differences from the mean. The variance for these hotel prices is \(2048.94\) dollars.

Step 4 ：The standard deviation is the square root of the variance. Therefore, the standard deviation for these hotel prices is \(\sqrt{2048.94} = 45.27\) dollars.

Step 5 ：\(\boxed{\text{Final Answer: The range of the hotel prices is \$130, the variance is \$2048.94, and the standard deviation is \$45.27.}}\)

Step 6 ：These measures of variation can be useful for someone searching for a room as they provide information about the spread and dispersion of the hotel prices. A high standard deviation, for example, indicates that the prices are spread out over a large range of values.