Measures Of Dispersion

Range = Largest Value

Range = Largest Value - Smallest Value. It's the simplest measure showing the total spread of data. For example, if test scores are 45, 67, 78, 89, 92

MD = (1/N) × Σ|xi

MD = (1/N) × Σ|xi - x̄| for ungrouped data, and MD = (1/N) × Σfi|xi - x̄| for grouped data. We take absolute values to avoid negative deviations cance

σ² = Σ(xi

σ² = Σ(xi - x̄)²/n for ungrouped data. Alternative formula: σ² = (Σxi²/n) - (Σxi/n)². For grouped data: σ² = Σfi(xi - x̄)²/N. We square deviations to

σ = √σ² (positive square root

σ = √σ² (positive square root of variance). It brings the measure back to original units. For example, if variance is 144 marks², then standard deviat

Used for grouped data with equal

Used for grouped data with equal class intervals. Steps: 1) Choose assumed mean 'a' (preferably middle class mark), 2) Calculate ui = (xi - a)/h where