Question

As gasoline prices have increased in recent years, many drivers have expressed concern about the taxes they pay on gasoline for their cars. In the United States, gasoline taxes are imposed by both the federal government and by individual states. The boxplot below shows the distribution of the state gasoline taxes, in cents per gallon, for all 50 states on January 1, 2006.

a) Based on the boxplot, what are the approximate values of the median and the interquartile range of the distribution of state gasoline taxes, in cents per gallon? Mark and label the boxplot to indicate how you found the approximated values.
b) The federal tax imposed on gasoline was 18.4 cents per gallon at the time the state taxes were in effect. The federal gasoline tax was added to the state gasoline tax for each state to create a new distribution of combined gasoline taxes. What are the approximate values, in cents per gallon, of the median and interquartile range of the new distribution of combined gasoline taxes? Justify your answer.

Answer 1

The approximate median state gasoline tax is 20 cents per gallon, with an approximate IQR of 10 cents per gallon. When the 18.4 cents per gallon federal tax is added, the new median becomes approximately 38.4 cents per gallon, and the IQR remains 10 cents per gallon.

Step-by-step explanation:

To answer the student's question regarding state gasoline taxes, we must analyze the provided boxplot for median and interquartile range (IQR). The median is the value separating the higher half from the lower half of the data set, and it is usually marked by a line within the box of the boxplot. The interquartile range is the range between the first quartile (25th percentile) and the third quartile (75th percentile), represented by the length of the box on a boxplot.

Without the actual boxplot, we approximate as follows: Assuming the median state gasoline tax is represented by a line within the box that appears to be around 20 cents per gallon, and the box length from approximately 15 to 25 cents per gallon suggests an IQR of about 10 cents per gallon.

Adding the federal gasoline tax of 18.4 cents per gallon to each value would increase both the median and each quartile by 18.4 cents. Therefore, the new median would be approximately 38.4 cents per gallon (20 + 18.4), and the IQR remains unchanged at 10 cents per gallon because the increase affects all parts of the distribution equally.