Question

question 3
for which one of the following distributions will the median be a better measure of center than
the mean?

• salary data for players in the national basketball association (nba) where most of the players earn the

league minimum and a few superstars earn very high salaries in comparison.

• repeated weight measurements of the same 1.6-ounce bag of peanut m&ms by students in a large

chemistry class using a balance scale.

• height data from a large random sample of men.
• exam scores with a central peak around an average test score and a few students scoring lower than the

average and a few scoring higher.

Explanation:

To determine when the median is a better measure of center than the mean, we analyze the distribution's skewness. The mean is affected by extreme values (outliers), while the median is resistant to them.

• Option 1 (NBA salaries): Most players have low salaries (league minimum), but a few superstars have extremely high salaries. This creates a right - skewed distribution (long tail on the high - value side). The mean will be pulled up by these high - salary outliers, so the median (which is the middle value and not affected by the extreme high salaries) is a better measure of the "typical" salary.
• Option 2 (M&M weight measurements): Repeated measurements of the same bag should be relatively symmetric around the true weight (1.6 ounces) with small random errors. In a symmetric distribution, the mean and median are approximately equal, so the mean is a good measure.
• Option 3 (Height data of men): Height data from a large random sample of men is typically approximately normally distributed (symmetric). In a symmetric distribution, the mean and median are close, so the mean is an appropriate measure.
• Option 4 (Exam scores): The distribution has a central peak with a few low and high scores. This is approximately symmetric (a few low and a few high scores, so the mean is not strongly affected by outliers), so the mean is a good measure.

Answer:

A. Salary data for players in the National Basketball Association (NBA) where most of the players earn the league minimum and a few superstars earn very high salaries in comparison.