Question

Which of the following statements is true of a measure of dispersion?

• A. Mean deviation does not follow algebraic value
• B. Range is crudest measure
• C. Coefficient of variation is a relative measure
• D. All the above statements

Answer 1

The correct option is D All the above statements

• Mean deviation is the arithmetic average of the deviations of the observed values from an average of the observed values. Since Mean deviation do not include negative value of the deviations. Therefore, it does not follow the algebraic value of the deviations.
  
• Range is defined as the difference between the highest(or largest ) and lowest(or smallest) observed value in a series. It is the most simple and commonly understandable measures of dispersion. Since it is the most affected measures of dispersion by the extreme values of the series, it is regarded as the crudest measure.
  
• Coefficient of variation is the coefficient of dispersion based on the standard deviation of the statistical series.Therefore, Coefficient of variation is a unit less or relative measure of dispersion as variation is the absolute measure of dispersion.