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Measures of Central Tendency — Economics STD 11 Commerce — Question

CBSE BoardEnglish MediumSTD 11 CommerceEconomicsMeasures of Central Tendency3 Marks
Question
State some special properties of the arithmetic mean.
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Answer

Some special properties of the arithmetic mean are:
  1. The sum of deviations of the observations from their arithmetic mean is always zero.
  2. The product of arithmetic mean and the number o values on which the mean is based equal to the sun of all given values. Symbolically,
$\text{n}\overline{\text{x}}=\sum\text{X}\ \Big[\because\overline{\text{x}}=\frac{\sum\text{X}}{\text{n}}\Big]$
  1. It is affected both by change in origin and change in scale.
  2. The sum of the squares of the deviation of a set of values is minimum when taken from mean.

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