behavioral · importance: medium
Mean vs Median vs Mode: When to Use Each
Mean, median, and mode are the three measures of "centre" — and choosing the wrong one is how charts mislead. Skewed data and outliers crush the mean but barely move the median, which is why housing-price reports almost always use median.
When the method applies
- • Question asks "average" without specifying
- • Data is skewed and the mean looks wrong
- • Multiple values appear equally often
- • Outliers shifting the answer
Common mistakes
- • Defaulting to mean for everything
- • Not checking for outliers or skew
- • Categorical data — mean does not even apply
Step-by-step method
- • Mean: sum / count. Good for symmetric data with no outliers.
- • Median: middle value when sorted. Use for skewed data (income, home prices).
- • Mode: most frequent value. Use for categorical data or to find peaks.
- • If outliers present: median is far more robust than mean.
- • Quick rule: news headlines should usually report median income / home price, not mean.
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Build long-term fluency
- • Always plot the data first (histogram or boxplot)
- • Compute all three for any dataset to see how skewed it is
- • Remember: a single billionaire ruins the mean of an income dataset
Edge cases & deeper reading
For multi-modal distributions (two peaks), reporting a single number is misleading — show the full distribution. For inferential statistics, the choice depends on whether the parametric model assumes normality.
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