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Consider the following statements: 1) The sum of deviations from mean is always zero. 2) The sum of absolute deviations is minimum when taken around median. Which of the above statements is/are correct?

Consider the following statements: 1) The sum of deviations from mean is always zero. 2) The sum of absolute deviations is minimum when taken around median. Which of the above statements is/are correct? Correct Answer Both 1 and 2

Concept:

Properties of mean deviation:

  • The sum of deviations from the mean is always zero, i.e., ∑(xi – x̅) = 0.
  • The sum of absolute deviations is minimum when taken around median.


Calculation:

Properties of mean deviation:

  • The sum of deviations from the mean is always zero, i.e., ∑(xi – x̅) = 0.
  • The sum of absolute deviations is minimum when taken around median.


So, statement (1) & statement (2) both are correct.

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