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? 79 78 174 194 108 106 278 180 The range of the sample data is (Round to one decimal place as needed.)

Step 1 ：Sort the data in ascending order: 78, 79, 106, 108, 174, 180, 194, 278

Step 2 ：Calculate the range by subtracting the smallest value from the largest value: 278 - 78 = \(\boxed{200}\)

Step 3 ：Calculate the variance, which is the average squared deviation of each number from the mean of the data set: \(\boxed{4215}\)

Step 4 ：Calculate the standard deviation, which is the square root of the variance: \(\boxed{65}\)

Step 5 ：The range of the data is \(\boxed{200}\), which means that the prices for one night at different hotels in the region vary by $200

Step 6 ：The variance of the data is approximately \(\boxed{4215}\) and the standard deviation is approximately \(\boxed{65}\), which means that the prices for one night at different hotels in the region vary by about $65 from the mean price

Step 7 ：These measures of variation can be useful for someone searching for a room because they provide information about the spread of the prices. A high variance and standard deviation indicate a wide spread of prices, which could mean that there are both very cheap and very expensive options available. A low variance and standard deviation indicate a narrow spread of prices, which could mean that most of the options are around the same price