A study of gasoline prices across a particular state showed that the state's mean gas price was $2.87 per gallon, and the median gas price was $3.25 per gallon. Which of the following most likely accounts for the difference between the mean and median gas prices in this state?

Options

A. A few areas of the state had substantially lower gas prices than the rest.
B. A few areas of the state had substantially highest gas prices than the rest.
C. The majority of areas of areas in the study has gas prices between $2.87 and $3.25 per gallon.
D. An error was made during data collection or data analysis.

Explanation

To solve the problem, we need to analyze the relationship between the mean and median gas prices and understand what could cause the difference between them.

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Mean gas price = $2.87 per gallon
- Median gas price = $3.25 per gallon

2. **Understand the Concepts of Mean and Median**:
- The mean is the average of all data points, calculated by adding all values and dividing by the number of values.
- The median is the middle value when all data points are arranged in ascending order. If there is an even number of values, it is the average of the two middle values.

3. **Analyze the Difference**:
- Here, the mean ($2.87) is less than the median ($3.25). This indicates that the distribution of gas prices is not symmetrical.

4. **Consider the Implications of Asymmetry**:
- In a symmetrical distribution, the mean and median are equal. When they differ, it suggests that the data is skewed.
- Since the mean is lower than the median, this typically indicates a left-skewed distribution, where there are some lower values (outliers) that pull the mean down.

5. **Identify the Role of Outliers**:
- Outliers are extreme values that differ significantly from other observations. They can be much higher or much lower than the rest of the data.
- In this case, the presence of lower outliers (significantly lower gas prices in some areas) could be affecting the mean, causing it to be lower than the median.

6. **Conclusion**:
- The difference between the mean and median gas prices is most likely due to the presence of a few areas in the state that have substantially lower gas prices than the majority of areas. This is why the mean is lower than the median.

### Final Answer:
The most likely reason for the difference between the mean and median gas prices in this state is that there are a few areas with substantially lower gas prices than the rest.

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