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Statistics · Ch 4 — Measures of Dispersion

Absolute and Relative Measures of Dispersion

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Absolute and Relative Measures of Dispersion

Measures of dispersion are classified into two broad types:

1. Absolute measures of dispersion are expressed in the same unit as the original data (rupees, marks, kilograms, etc.). Range, Quartile Deviation, Mean Deviation, and Standard Deviation are all absolute measures. They are useful when comparing the variability of two series measured in the same unit and having similar average values.

2. Relative measures of dispersion (also called coefficients of dispersion) are pure, unit-free numbers obtained by dividing an absolute measure by an appropriate average. Because they carry no unit, relative measures are used to compare the variability of:

  • two series expressed in different units (e.g., comparing variability of height in cm with variability of weight in kg), or
  • two series with very different averages (e.g., comparing the wage variability of a factory paying an average of Rs. 500/day with one paying an average of Rs. 5,000/day).
Absolute measureCorresponding relative measure (coefficient)
RangeCoefficient of Range =L−SL+S=\dfrac{L-S}{L+S}
Quartile DeviationCoefficient of Q.D. =Q3−Q1Q3+Q1=\dfrac{Q_3-Q_1}{Q_3+Q_1}
Mean DeviationCoefficient of M.D. =M.D.Average used=\dfrac{\text{M.D.}}{\text{Average used}}