A national restaurant chain is composed of 6500 restaurants, each of which is located in close proximity to an interstate highway. The restaurant's business strategy is to serve its core customer base: people travelling on the interstate highway system who are looking for a quality dining experience. Customers generally enjoy the restaurant chain's menu, atmosphere, and consistency from restaurant to restaurant. The company's leadership, located at corporate headquarters, is very interested in the relationship between the cost of a gallon of gasoline and the company's revenue. Specifically, the company is concerned that if gasoline prices rise in the near future, the company's revenue will decline dramatically. The company's research department recently collected data for analysis in order to support leadership's upcoming discussion of whether the company should expand and diversify to locations away from an interstate highway. Annual revenue figures from a random sample of 150 restaurants were collected. The research division also collected and calculated the average annual cost of gasoline at these 150 restaurants by randomly selecting three gasoline stations near each restaurant Historical data was then used to calculate the average annual cost of gasoline. The Restaurant Number, Geographic Region, Annual Revenue, Average Cost of Gasoline, Miles from the Interstate, Square Footage and Annual Increase in Revenue were collected for these 150 restaurants. StatCrunch Data Set Based upon your visual analysis of the Average Cost of Gasoline histogram, what is the most appropriate measure of center and variation to calculate and interpret? The mean and Interquartile Range because the shape of the distribution is symmetrical. The median and standard deviation because the shape of the distribution is skewed. The mean and standard deviation because the shape of the distribution is symmetrical. The median and Interquartile Range because the shape of the distribution is skewed
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When examining the Average Cost of Gasoline histogram, if the shape of the distribution is skewed, the median is the best measure of center as it is robust to outliers. Additionally, using the Interquartile Range (IQR) for variation helps to understand the spread of values without being affected by extreme values, providing a clearer picture of typical gasoline costs near those restaurants. Understanding how gasoline prices impact revenue is vital for strategic decision-making. If gasoline costs rise, it may deter travelers from dining out frequently, especially if they perceive the associated travel expense as too high. This insight encourages the company to consider diversifying its location strategy to better cater to varied customer demographics, thereby mitigating the risks linked to fluctuating fuel prices.