A magazine 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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Part 1
Choose the correct answer below.
A.
​No, the value of 27.3 cents is not the mean because the 50 amounts are all weighted equally in the​ calculation, but some states consume more gas than​ others, so the mean amount of state sales tax should be calculated using a weighted mean.
B.
​Yes, the value of 27.3 cents is the mean because a mean is found by summing all sample values and then dividing the by total number of values.
C.
​No, the value of 27.3 cents is not the mean because it is the median that is found by summing all sample values and then dividing the by total number of values.
D.
​Yes, the value of 27.3 cents is the mean because it is a measure of center and all measures of centers can be refered to as either an average or a mean. 

The correct answer is:

**A.** No, the value of 27.3 cents is not the mean because the 50 amounts are all weighted equally in the calculation, but some states consume more gas than others, so the mean amount of state sales tax should be calculated using a weighted mean.

### Explanation:
While 27.3 cents represents the arithmetic mean (or average) of the state tax amounts, it does not account for the fact that states vary significantly in how much gasoline they consume. In states with higher gas consumption, the total tax collected would be higher, which should affect the overall average tax paid by drivers. To get a more accurate picture of what the average driver in the U.S. is paying in state gas taxes, a **weighted mean** should be used, where the amount of gas consumed in each state acts as the weight.

Would you like more details on how weighted means work or have any other questions?

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Here are 5 related questions for further exploration:
1. What is the difference between an arithmetic mean and a weighted mean?
2. How can we calculate a weighted mean when given weights and values?
3. Why do some states consume more gasoline than others?
4. How would the median value of state gas taxes compare to the mean?
5. How could outliers in state taxes affect the arithmetic mean?

**Tip:** When working with averages in real-world data, consider whether the data points should be weighted to reflect real-world conditions better.

A magazine 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? Choose the correct answer below.
A. No, the value of 27.3 cents is not the mean because the 50 amounts are all weighted equally in the​ calculation, but some states consume more gas than​ others, so the mean amount of state sales tax should be calculated using a weighted mean.
B. Yes, the value of 27.3 cents is the mean because a mean is found by summing all sample values and then dividing by the total number of values.
C. No, the value of 27.3 cents is not the mean because it is the median that is found by summing all sample values and then dividing by the total number of values.
D. Yes, the value of 27.3 cents is the mean because it is a measure of center and all measures of centers can be referred to as either an average or a mean.

Explore whether 27.3 cents is the true mean of state gas taxes paid by U.S. drivers. This problem explains the difference between arithmetic mean and weighted mean, highlighting the importance of weighting based on gasoline consumption in different states. Suitable for students in Grades 9-12.

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