USA Today published a list consisting of the state tax on...

USA Today published a list consisting of the state tax on each gallon of gas. If we add the 50 state tax amounts and then divide by $50,$ we get 27.3 cents. Is the value of 27.3 cents the mean amount of state sales tax paid by all U.S. drivers? Why or why not?

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Key Concepts

Population Weighting

Population weighting involves adjusting the contribution of each state’s tax rate based on the number of drivers or the amount of gasoline consumed in that state. This is crucial in determining an average that represents the actual tax burden on all drivers, whereas an unweighted mean may mislead because it treats all states as having equal impact regardless of driver population or usage.

Arithmetic Mean

The arithmetic mean is calculated by summing a set of values and dividing by the number of values. In the question, summing the state tax amounts and dividing by 50 provides the arithmetic mean of the state tax rates, which is a straightforward average without additional factors.

Weighted Average

A weighted average takes into consideration the relative importance or frequency of each value. In the context of state sales tax paid by drivers, different states have varying numbers of drivers and different levels of gas consumption. Therefore, simply averaging the state tax rates without weighting by these factors does not accurately reflect the average tax amount paid by all drivers.

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