Questions: Mean, Median, and Mode

Question 1

A company has 9 employees earning $40,000/year and 1 CEO earning $1,000,000/year. Which measure best represents a 'typical' employee's salary?

• A. Mean, because it uses all the data
• B. Median, because it is resistant to the outlier
• C. Mode, because it appears most often
• D. Mean and median are always equal, so it doesn't matter

Answer: (B)

The mean salary would be about $136,000 — far above what any regular employee earns — because the CEO's salary pulls it up dramatically. The median ($40,000) is resistant to that outlier and accurately reflects the typical employee's pay. This is exactly why news reports on income often cite median household income rather than mean.

Question 2

For the data set {3, 5, 5, 7, 9}, the mean and median are equal.

• T. True
• F. False

Answer: False

The mean is (3+5+5+7+9)/5 = 29/5 = 5.8. The median is the middle value when ordered: 5. They are not equal. The mean and median coincide only in perfectly symmetric distributions — in this data set, the higher values pull the mean above the median.

Question 3

A data set has no value that appears more than once. What is the mode, and what does this tell you about using mode as a summary statistic here?

Model answer: There is no mode (or every value is a mode, depending on convention). This shows that mode is a poor summary statistic for continuous or spread-out data — it only works well when data clusters at specific repeated values.

Mode is most useful for categorical or discrete data with natural clusters (e.g., shoe sizes, survey responses). When every value is unique, mode tells you nothing about the center of the distribution.