Relative position of mean, median and mode

Indian Economy glossary

Topic: Economic Data: Census, NSS, Surveys and Statistical Tools · NCERT: Class 11, Ch 5 "Measures of Central Tendency"

Meaning

The relative position of the mean, median and mode depends on the shape of the distribution.

  • In a symmetric distribution, where both sides mirror each other, all three are equal.
  • In a moderately skewed distribution, which has one peak and a tail stretched to one side, the median usually lies between the mean and the mode. Karl Pearson's rule links the three: Mode ≈ 3 Median − 2 Mean.

This rule holds only for moderately skewed data with a single peak. It is not true for every distribution.

Example

Income is right-skewed: most people earn modest amounts, and a few earn very large amounts. So mean > median > mode, because the rich pull the mean upward. This is why per capita income overstates what a typical Indian earns, and why the median is the better guide.

Don't confuse with

  • "Median always lies between mean and mode": this is not always true. It holds only for moderately skewed data with a single peak.

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