Arithmetic mean

Indian Economy glossary

Also called: Mean, Average · Topic: Economic Data: Census, NSS, Surveys and Statistical Tools · NCERT: Class 11, Ch 1 "Introduction (Statistics for Economics)"; Class 11, Ch 5 "Measures of Central Tendency"; Class 11, Ch 8 "Use of Statistical Tools"

Meaning

The arithmetic mean is the sum of all observations divided by their number. It is the most common "average".

X̄ = ΣX / N

For grouped data, X̄ = Σfm / Σf, where m is the class mark, i.e. the midpoint of each class.

Its main properties:

  • It uses every value.
  • Deviations from it always add up to zero: Σ(X − X̄) = 0.
  • An extreme value (an outlier) pulls it up or down.
  • It cannot be computed when there are open-ended classes such as "70 and over".

Example

Five farmers in Manipur earn 500, 550, 600, 650 and 700. The mean is 3,000 ÷ 5 = 600. Now take the series 1, 2 and 3,000. Its mean is 1,001, which is not typical of any of the values. This is why per capita income can overstate what a typical person earns.

Don't confuse with

  • Median: this is the middle value of ordered data. Outliers barely affect it, so it is the better average for skewed data such as incomes.

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