Skewness
Skewness describes lopsided data. Right-skewed data has a long tail of large values. Left-skewed data has a long tail of small values. The mean gets pulled toward the tail.
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Analogy
Imagine a seesaw with a few heavy people far out on one side. The balance point (the mean) shifts toward them.
Example
House prices (thousands):150, 160, 170, 180, 900Median = 170Mean = 1560 / 5 = 312Mean > median: right skew
In practice
Incomes are right-skewed, so the mean income is higher than the median income.
Practice
Flashcards
- Mean greater than median suggests what shape?Right skew: a long tail of large values.
Interview questions
- Data on household income has mean 52,000 and median 41,000. What does this tell you and which would you report?
- Mean above median suggests right skew
- A few high incomes pull the mean up
- Median is a better typical value
- Reporting both shows the gap
Questions people ask
How can you tell skew from the mean and median?
Compare them. If the mean is clearly larger than the median, the data is right-skewed. If the mean is clearly smaller, it is left-skewed. If they are about equal, the data is roughly symmetric. A histogram shows the same thing by eye.
Which average should I report for skewed data?
Report the median, because it stays near the typical value while the mean is dragged toward the tail. Many analysts give both, so readers see the gap. For symmetric data with no outliers, the mean is fine and works better in later calculations.