Questions: 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? 290 100 197 171 213 248 259 77 The range of the sample data is (Round to one decimal place as needed.)

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? 290 100 197 171 213 248 259 77 The range of the sample data is (Round to one decimal place as needed.)
Transcript text: 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? 290 100 197 171 213 248 259 77 The range of the sample data is $\square$ $\square$ (Round to one decimal place as needed.)
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Solution

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Solution Steps

Step 1: Calculate the Range

To calculate the range, we find the maximum and minimum values in the data set.

Maximum price: $290 Minimum price: $77

Range = max - min = $290 - $77 = $213

Step 2: Calculate the Variance

The variance is calculated by first finding the mean of the data set, then computing the squared difference from the mean for each data point, and finally averaging these squared differences.

Mean price = Sum of all prices / Number of observations = $194.4

Variance = Sum of squared differences / (n - 1) = $5682.8

Step 3: Calculate the Standard Deviation

The standard deviation is the square root of the variance.

Standard Deviation = sqrt(Variance) = $75.4

Final Answer:

The range of the hotel prices is $213, indicating the spread between the cheapest and most expensive options.

The variance of the hotel prices is $5682.8, and the standard deviation is $75.4, indicating how much the prices vary from the average price.

These measures of variation can help someone searching for a room understand the diversity in pricing within the region, aiding in budget planning and expectation setting.

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