Suppose you were in charge of advertising for an automotive dealership when the gas prices increased to $4 per gallon. Most of your cars are fuel-efficient, but you have two models that have extremely poor fuel economy, that is, a low number of miles per gallon. How would you use a measure of central tendency in your advertising to present your product line in the best light? Why would you choose this measure of central tendency? What circumstances would make you choose an alternative measure? Specify the circumstances and the measure you would use.

To use a measure of central tendency in advertising, you would want to choose a measure that best represents the typical fuel economy of your product line. In this case, the two models with extremely poor fuel economy might not be the most representative examples of your product line, so you would likely omit these models from your analysis.

Common measures of central tendency include the mean, median, and mode. Let's consider each one and how you could use them in your advertising:

1. Mean: The mean is calculated by summing up all the fuel economy values for the remaining models and dividing by the number of models. This measure is useful when you want to present an average fuel economy value. In advertising, you might say something like, "Our product line has an average fuel economy of X miles per gallon." However, using the mean might be misleading if a few highly fuel-efficient models significantly bring up the average, while many models have lower fuel economy. In this case, the mean might not be the best option.

2. Median: The median is the middle value when all fuel economy values are sorted in ascending order. This measure is useful when you want to present a value that represents the midpoint of your product line's fuel economy. In advertising, you might say something like, "The median fuel economy of our product line is X miles per gallon," which indicates that half of your models have fuel economy above that value. The median is less sensitive to outliers and may provide a more representative measure of central tendency if you have a few models with significantly different fuel economy.

3. Mode: The mode is the most frequent fuel economy value in your product line. This measure is useful when you want to highlight a particular fuel economy value that is most common in your lineup. In advertising, you might say something like, "Our product line features a mode fuel economy of X miles per gallon," which indicates the most popular fuel economy value. However, if you have a diverse product line with no clear peak in the fuel economy values, the mode may not be a useful measure.

The choice of which measure to use ultimately depends on the characteristics of your product line and your advertising goals. If you have a relatively homogeneous product line with minor variations in fuel economy, the mean might be suitable. However, if you have a more diverse product line with some outliers, the median could be a better choice as it is less affected by extreme values. The mode is the best option if you want to emphasize a specific fuel economy value that is popular among your models.

In the given scenario, since most of your cars are fuel-efficient, you may choose to utilize the median fuel economy as a measure of central tendency in your advertising. This decision is based on the assumption that the two extremely poor fuel economy models are not representative of your product line and might not align with your target audience's preferences. Consequently, by using the median, you can present a fuel economy value that is more typical and accurately represents the majority of your cars.