In which of the following situations will the mean value and median value of variable be meaningfully different?

Question

Options

• AWhen the variable contains no outliers
• BWhen the variable contains no missing values
• CWhen the variable is of the boolean type
• DWhen the variable is of the categorical type
• EWhen the variable contains a lot of extreme outliers

• B
  3% (1)
• C
  3% (1)
• D
  10% (3)
• E
  83% (25)

Explanation

Option E is correct because extreme outliers pull the mean toward them (since mean sums all values), while the median - the middle value - remains largely unaffected. For example, if 9 people earn $30k and 1 earns $1M, the mean skyrockets while the median stays near $30k, creating a meaningful gap between the two.

Why the distractors are wrong:

• A - No outliers means the distribution is likely symmetric, so mean ≈ median.
• B - Missing values affect sample size but don't inherently cause mean/median divergence.
• C - Boolean (true/false) variables have a mean that equals the proportion of true values, which is also a valid central tendency; the median will be 0 or 1, but this isn't a meaningful difference in the way the question intends - there's no skew dynamic.
• D - Categorical variables have no natural ordering, so calculating a mean is mathematically meaningless; the comparison itself doesn't apply.

Memory tip: Think of billionaires in a room - one Jeff Bezos raises the mean income dramatically, but the median barely moves. Outliers drag the mean; the median holds its ground. "Mean is sensitive, median is stubborn."

No community discussion yet for this question.