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.

186

213

75

188

158

280

197

Range = 205 dollars

Variance = 3255.9 square dollars

Standard deviation = 57.06 dollars

Explanation:

Range = highest price - lowest price = 280 - 75 = 205 dollars

Mean = summation of prices ÷ number of hotels = (186+213+75+188+158+280+197) ÷ 7 = 1297 ÷ 7 = 185.3 dollars

Variance = (summation of square of the difference between each price and mean) ÷ number of hotels = [(186-185.3)^2 + (213-185.3)^2 + (75-185.3)^2 + (188-185.3)^2 + (158-185.3)^2 + (280-185.3)^2 + (197-185.3)^2] ÷ 7 = 22791.43 ÷ 7 = 3255.9 square dollars

Standard deviation = sqrt(variance) = sqrt(3255.9 square dollars) = 57.06 dollars

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