Question

consider the following salaries for the executives of a certain company.
position\tsalary
president\t$190,000
1st vp\t$140,000
2nd vp\t$110,000
supervising manager\t$56,000
accounting manager\t$50,000
personnel manager\t$50,000
department manager\t$30,000
department magager\t$30,000
which measure seems to best describe the average executive salary for the company?
○ the median is most descriptive.
○ the mean is most descriptive.
○ the mode is most descriptive.

Explanation:

Step1: Analyze Data Distribution

The salaries are: $190,000, $140,000, $110,000, $56,000, $50,000, $50,000, $30,000, $30,000. There are extreme values (like $190k, $140k) that can skew the mean. The median is less affected by outliers. The mode (30k, 50k) doesn't represent the "middle" well here.

Step2: Compare Mean, Median, Mode

• Mean: Sum all salaries and divide by 8. Sum = \(190000 + 140000 + 110000 + 56000 + 50000 + 50000 + 30000 + 30000 = 656000\). Mean = \(656000\div8 = 82000\). But most salaries are below 82k (only 3 salaries above, 5 below), so mean is skewed by high outliers.
• Median: Order data: 30k, 30k, 50k, 50k, 56k, 110k, 140k, 190k. Middle two: 50k and 56k. Median = \((50000 + 56000)\div2 = 53000\), which is closer to most salaries (5 of 8 are ≤56k).
• Mode: 30k and 50k (bimodal), not representative of the "average" as it's just the most frequent, not the center.

Answer:

The median is most descriptive.