Measures of dispersion

Indian Economy glossary

Also called: Dispersion · Topic: Economic Data: Census, NSS, Surveys and Statistical Tools · NCERT: Class 11, Ch 2 "Collection of Data"; Class 11, Ch 8 "Use of Statistical Tools"

Meaning

Measures of dispersion show how widely the values in a data set are spread around their average. Two sets can have the same average but very different spreads, so an average means little without a measure of spread. The main measures are:

  • Range: the largest value minus the smallest.
  • Mean deviation: the average absolute distance from the mean or the median.
  • Variance: σ² = Σ(X − X̄)²/N.
  • Standard deviation: σ = √variance. It is in the same units as the data.

Example

In NCERT's toothpaste project, mean monthly family income was Rs 18,000 and the standard deviation was Rs 9,000, so incomes varied a lot. NCERT also tells of a family who crossed a river because its average depth was less than their average height. The children drowned, because the average hid the deep spots.

Don't confuse with

  • Measures of central tendency: these give one typical value. Dispersion measures the spread around that value.

Related concepts

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