Measures of Dispersion

Answer

Dispersion is a measure that shows how far the observations of data are scattered from the measure of average (central tendency). It is important because: • Measures of central tendency alone are insu…

Answer

**Absolute Measure:** • Expressed in same units as original data • Cannot compare variability of different units • Example: If data is in kg, measure is also in kg **Relative Measure:** • Free from u…

Answer

**Range (R):** Difference between highest and lowest observation **Formula:** R = xₕ - xₗ where xₕ = highest value, xₗ = lowest value **Advantages:** • Simple to calculate and understand • Clearly de…

Answer

**Coefficient of Range:** The relative measure of range, which is unit-free and used for comparison. **Formula:** Coefficient of Range = (xₕ - xₗ)/(xₕ + xₗ) where: • xₕ = highest observation • xₗ = …

Answer

**Quartile Deviation (Qd):** Measure of dispersion based on middle 50% of observations arranged in ascending order. **Formula:** Qd = (Q₃ - Q₁)/2 where Q₃ = third quartile, Q₁ = first quartile **Why…

Answer

**Advantages:** • Clearly defined measure • Simple computation • Not affected by extreme values (uses middle 50% only) • Can be calculated for open-ended classes • Based on position, not affected by o…

Answer

**Coefficient of Quartile Deviation:** Formula = (Q₃ - Q₁)/(Q₃ + Q₁) where: • Q₃ = Third quartile • Q₁ = First quartile This is a relative measure, unit-free, and used for comparing variability bet…

Answer

**Mean Deviation (MD):** The mean of absolute deviations of all observations from their mean. **Formula for Ungrouped Data:** MD = Σ|xi - x̄|/n where: • xi = individual observations • x̄ = mean of t…