Question

choose the best answer to the following question explain your reasoning
the distribution of wages at a company is right - skewed with outliers at high values assuming you would like a high wage would you hope that your wage was closer to the mean, median or mode?

choose the correct answer below
a. it should be closer to the mode because the mode is always higher than the mean and median
b. it should be closer to the mean because the mean is always higher than the median and mode
c. it should be closer to the mean because the mean is greater than the median and mode when the distribution is right - skewed
d. it should be closer to the median because the median is greater than the mean and mode when the distribution is right - skewed
e. it should be closer to the median because the median is always higher than the mean and mode
f. it should be closer to the mode because the mode is greater than the mean and median when the distribution is right - skewed

Explanation:

In a right - skewed distribution (with outliers at high values), the mean is pulled up by the high - value outliers. So, the mean is greater than the median, and the mode is the most frequently occurring value (usually the lowest among mean, median, mode in right - skewed).

• Option A: Mode is not always higher; in right - skewed, mode is usually lowest. Eliminate.
• Option B: “Always” is wrong. Mean is higher in right - skewed, but not always in all cases (but in this context of right - skewed with high outliers, mean is higher). But option C is more accurate as it specifies the distribution type.
• Option C: Correct. In right - skewed distribution, mean > median > mode (in general for right - skewed with high outliers), so to have a high wage, being closer to mean (the highest of the three) is better.
• Option D: Median is not greater than mean in right - skewed. Eliminate.
• Option E: Median is not always higher. Eliminate.
• Option F: Mode is not greater in right - skewed. Eliminate.

Answer:

C. It should be closer to the mean because the mean is greater than the median and mode when the distribution is right - skewed